Question 1

Solve the problem.
-The value of a particular investment follows a pattern of exponential growth. In the year 2000, you invested money in a money market account. The value of your investment t years after 2000 is given by the exponential
Growth model  How much did you initially invest in the account?
A) $4700.00
B) $2350.00
C) $291.40
D) $5000.62

Accepted Answer

The answer of Solve the problem.
-The value of a particular...

Question 2

Solve the problem.
-The function f(x) = 1 + 1.5 ln (x+1) models the average number of free-throws a basketball player can make consecutively during practice as a function of time, where x is the number of consecutive days the basketball
Player has practiced for two hours. After 402 days of practice, what is the average number of consecutive free
Throws the basketball player makes?
A) 10 consecutive free throws
B) 13 consecutive free throws
C) 11 consecutive free throws
D) 14 consecutive free throws

Accepted Answer

The answer of Solve the problem.
-The function f(x) = 1...

Question 3

Solve the problem.
-The long jump record, in feet, at a particular school can be modeled by f(x) = 18.1 + 2.5 ln (x + 1) where x is the number of years since records began to be kept at the school. What is the record for the long jump 16 years after
Records started being kept? Round your answer to the nearest tenth.
A) 24.9 ft
B) 20.6 ft
C) 25.0 ft
D) 25.2 ft

Accepted Answer

To find the long jump record 16 years after records began, substitute x = 16 into the given function: f(16) = 18.1 + 2.5 ln(16 + 1) = 18.1 + 2.5 ln(17). Calculating this gives approximately 25.2 feet.

Question 4

Solve the problem.
-The population of a particular country was 24 million in 1980; in 1994, it was 32 million. The exponential growth function  describes the population of this country t years after 1980. Use the fact that 14 years
After 1980 the population increased by 8 million. Find k rounded to three decimal places.
A) 0.475
B) 0.149
C) 0.021
D) 0.031

Accepted Answer

Using the given information, we know that:

1980 population = 24 million
1994 population = 32 million
Population increased by 8 million in 14 years.

Using the exponential growth function:

32 = 24e^(k*14)

Solving for k:

ln(32/24) = k*14
ln(4/3) = 14k
k = ln(4/3)/14 ≈ 0.021

Therefore, the answer is C) 0.021. We can use the information given to set up two equations:

11ebb63d_1bdc_13f4_b851_154841fca473_TB8475_12  = 24e^k(0) = 24
11ebb63d_1bdc_13f4_b851_154841fca473_TB8475_13  = 32e^k(14)

We want to find k such that the population increased by 8 million over 14 years. That means:

32e^k(14) - 24e^k(0) = 8
e^14k = 1.33333...
14k ≈ ln(1.33333...)
k ≈ 0.0205

Rounded to three decimal places, the answer is 0.021. Therefore, the answer is C.

Question 5

Solve the problem.
-The function  models the amount in pounds of a particular radioactive material stored in a concrete vault, where t is the number of years since the material was put into the vault. If 600 pounds of the
Material are placed in the vault, how much time will need to pass for only 106 pounds to remain? Round to the
Nearest year.
A) 150 yr
B) 155 yr
C) 300 yr
D) 160 yr

Accepted Answer

The answer of Solve the problem.
-The function  models the...

Question 6

Solve the problem.
-If $7000 is invested at 8% compounded continuously, determine the balance in the account after 3 years.
A) $8898.74
B) $8817.98
C) $8680.00
D) $8998.74

Accepted Answer

The formula for continuous compounding is $A = Pe^{rt}$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (decimal), and $t$ is the time the money is invested for in years. Plugging in the given values: $A = 7000e^{0.08*3}$, we get $A = 7000e^{0.24}$, which calculates to approximately $8898.74.

Question 7

Solve the problem.
-The function  models the amount in pounds of a particular radioactive material stored in a concrete vault, where t is the number of years since the material was put into the vault. If 400 pounds of the
Material are initially put into the vault, how many pounds will be left after 190 years? Round to the nearest
Pound.
A) 422 lb
B) 95 lb
C) 288 lb
D) 93 lb

Accepted Answer

The answer of Solve the problem.
-The function  models the...

Question 8

Solve the problem.
-The value of a particular investment follows a pattern of exponential growth. In the year 2000, you invested money in a money market account. The value of your investment t years after 2000 is given by the exponential
Growth model A  . By what percentage is the account increasing each year?
A) 5.9%
B) 5.4%
C) 5.6%
D) 5.8%

Accepted Answer

The answer of Solve the problem.
-The value of a particular...

Question 9

Solve the problem.
-The value of a particular investment follows a pattern of exponential growth. In the year 2000, you invested money in a money market account. The value of your investment t years after 2000 is given by the exponential
Growth model A  When will the account be worth $2834?
A) 2010
B) 2007
C) 2009
D) 2008

Accepted Answer

The answer of Solve the problem.
-The value of a particular...

Quiz 13: Exponential and Logarithmic Functions

Solve the problem. -If $7000 is invested at 8% compounded continuously, determine the balance in the account after 3 years.

Solve the problem. -The value of a particular investment follows a pattern of exponential growth. In the year 2000, you invested money in a money market account. The value of your investment t years after 2000 is given by the exponential Growth model A When will the account be worth $2834?