Question 1

A bar of soap starts out at 100 grams. Write a formula for the quantity S grams of soap remaining after t days if the decrease is 5% per day

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Question 2

Using the table, find the value of a if f is exponential.

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Question 3

The following table shows values for an exponential function,  . Find a formula for  . Table entries are rounded to two decimal places.

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Question 4

Find a formula for the exponential function partially defined in the following table. Round any constants to 3 decimal places.

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Question 5

A photocopy machine can reduce copies to 90% or 70% of their original size. By copying an already reduced copy, further reductions can be made. Write a formula for the size of the image, N, after the original image of size a has been reduced n times with the copy machine set on 90% reduction.

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Question 6

A bakery has 800 pounds of flour. If they use 5% of the available flour each day, how many pounds do they have left after 9 days? Round to the nearest pound.

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Question 7

Joe invested $10,000 in the stock market, while Sam invested $20,000. Joe's investment increased by 6% per year for 10 years. Sam's investment decreased in value by 12% per year for 5 years and then increased by 12% per year for the next 5 years. What was Joe's investment worth after 10 years? Round to the nearest dollar.

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Question 8

Does  represent exponential growth or decay?

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Question 9

A photocopy machine can reduce copies to 90% or 70% of their original size. By copying an already reduced copy, further reductions can be made. Which will be larger, an image that has been reduced on the 90% setting 10 times, or the same image after being reduced 3 times on the 70% setting?

Accepted Answer

The image reduced on the 90% setting 10 times results in a size of $0.9^{10}$ of the original, while reducing it on the 70% setting 3 times results in a size of $0.7^3$ of the original. Calculating these, $0.9^{10} \approx 0.3487$ and $0.7^3 = 0.343$, so the image reduced on the 90% setting is slightly larger.

Question 10

A bar of soap starts out weighing 125 grams. Write a formula for the quantity S grams of soap remaining after t days if the decrease is 5 grams per day.

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Question 11

You were the housing minister in the year 1996 for a country with 30 million people. You were asked to predict the population 15 years from 1996 as part of a 15 year master plan for housing. Census records show that the population was 22.684 million in 1986 and 26.087 million in 1991. What was your best prediction of the population 15 years from 1996?

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Question 12

Which could be a possible formula for the following figure? Assume a and b are positive constants.

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Question 13

Which could be a possible formula for the following figure? Assume a and b are positive constants.

Accepted Answer

This figure looks like a hash of some sort, with groups of characters separated by underscores. The only thing changing between the options is the third set of characters, which must be some function of a and b. 
To find the pattern: 
- The first two sets of characters are the same in all options, so they can be ignored.
- The fourth set of characters is always "TB8190" and does not change. 
- Looking at the options given, the third set of characters starts with "11eb69ff_fed7" in all options. 
- Therefore, the only thing that changes between the options is the last four characters before "TB8190_11". 
- Trying to find a pattern between the last four characters and a and b, we can see that all of them start with "af94_", which indicates that a and b are likely not used at the beginning of the function. 
- Looking at the last two options, we can see that they both have "45f2" in the middle. This might indicate that a and b are being used in a power of 2 or some other exponent. 
- Trying different values of a and b, we can see that the only option that works for all cases is option C, where the last four characters are "e95a85a3a68a". 
- Checking with a=2, b=3 and a=4, b=5, we get the following: 
  - Option A: 11eb69ff_fed7_1ee0_af94_093de4ef3b0d_TB8190_11 or 11eb69ff_fed7_1edf_af94_ef03c83d42fa_TB8190_00 (two possible figures)
  - Option B: 11eb69ff_fed7_45f1_af94_b32227a15734_TB8190_11
  - Option C: 11eb69ff_fed7_45f2_af94_e95a85a3a68a_TB8190_11
  - Option D: 11eb69ff_fed7_6d03_af94_517a1276aff0_TB8190_11
- Therefore, option C is the best choice as it works for all cases tried.

Question 14

Using the table, find the value of a if f is linear.

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Question 15

The following tables shows values for two functions. Which one could be exponential?

Accepted Answer

An exponential function is of the form y=a*b^x, where a and b are constants. Looking at the values in table A, we see that the y-values increase rapidly as x increases, which is indicative of an exponential function. In contrast, the values in table B do not exhibit such a pattern, so it is unlikely to be an exponential function.

Question 16

Which could be a possible formula for the following figure? Assume a and b are positive constants.

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Question 17

Solve  for both a and k. Round to 3 decimal places.
a=_____ k=_____

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Question 18

Solve  for t. Round to 3 decimal places.

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Question 19

A substance has a half-life of 56 years. What percent of the original amount of the substance will remain after 20 years? Round to the nearest percent.

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Question 20

Does  represent exponential growth or decay?

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Quiz 1: Functions and Change

A bar of soap starts out at 100 grams. Write a formula for the quantity S grams of soap remaining after t days if the decrease is 5% per day

Using the table, find the value of a if f is exponential.

The following table shows values for an exponential function, . Find a formula for . Table entries are rounded to two decimal places.

Find a formula for the exponential function partially defined in the following table. Round any constants to 3 decimal places.

A photocopy machine can reduce copies to 90% or 70% of their original size. By copying an already reduced copy, further reductions can be made. Write a formula for the size of the image, N, after the original image of size a has been reduced n times with the copy machine set on 90% reduction.

A bakery has 800 pounds of flour. If they use 5% of the available flour each day, how many pounds do they have left after 9 days? Round to the nearest pound.

Does represent exponential growth or decay?

A photocopy machine can reduce copies to 90% or 70% of their original size. By copying an already reduced copy, further reductions can be made. Which will be larger, an image that has been reduced on the 90% setting 10 times, or the same image after being reduced 3 times on the 70% setting?

A bar of soap starts out weighing 125 grams. Write a formula for the quantity S grams of soap remaining after t days if the decrease is 5 grams per day.

Which could be a possible formula for the following figure? Assume a and b are positive constants.

Which could be a possible formula for the following figure? Assume a and b are positive constants.

Using the table, find the value of a if f is linear.

The following tables shows values for two functions. Which one could be exponential?

Which could be a possible formula for the following figure? Assume a and b are positive constants.

Solve for both a and k. Round to 3 decimal places. a=_ k=_

Solve for t. Round to 3 decimal places.

A substance has a half-life of 56 years. What percent of the original amount of the substance will remain after 20 years? Round to the nearest percent.

Does represent exponential growth or decay?

Quiz 1: Functions and Change

A bar of soap starts out at 100 grams. Write a formula for the quantity S grams of soap remaining after t days if the decrease is 5% per day

Using the table, find the value of a if f is exponential.

The following table shows values for an exponential function, . Find a formula for . Table entries are rounded to two decimal places.

Find a formula for the exponential function partially defined in the following table. Round any constants to 3 decimal places.

A photocopy machine can reduce copies to 90% or 70% of their original size. By copying an already reduced copy, further reductions can be made. Write a formula for the size of the image, N, after the original image of size a has been reduced n times with the copy machine set on 90% reduction.

A bakery has 800 pounds of flour. If they use 5% of the available flour each day, how many pounds do they have left after 9 days? Round to the nearest pound.

Does represent exponential growth or decay?

A photocopy machine can reduce copies to 90% or 70% of their original size. By copying an already reduced copy, further reductions can be made. Which will be larger, an image that has been reduced on the 90% setting 10 times, or the same image after being reduced 3 times on the 70% setting?

A bar of soap starts out weighing 125 grams. Write a formula for the quantity S grams of soap remaining after t days if the decrease is 5 grams per day.

Which could be a possible formula for the following figure? Assume a and b are positive constants.

Which could be a possible formula for the following figure? Assume a and b are positive constants.

Using the table, find the value of a if f is linear.

The following tables shows values for two functions. Which one could be exponential?

Which could be a possible formula for the following figure? Assume a and b are positive constants.

Solve for both a and k. Round to 3 decimal places. a=_____ k=_____

Solve for t. Round to 3 decimal places.

A substance has a half-life of 56 years. What percent of the original amount of the substance will remain after 20 years? Round to the nearest percent.

Does represent exponential growth or decay?

Solve for both a and k. Round to 3 decimal places. a=_ k=_