Question 1

For the consumption function C = 10 +  
I -  
,
(a)find the marginal propensity to consume when I = 16;
(b)find the marginal propensity to save with I = 16.

Accepted Answer

The answer of For the consumption function C = 10...

Question 2

Find the derivative of y =  
.

Accepted Answer

The answer of Find the derivative of y = ...

Question 3

A bus company will plan a group trip for groups of 10 or larger.If the group is exactly 10,the cost is $50 per person.The company offers to discount each person's ticket by $2 for each addition to the group above 10.The revenue for the bus company is given by: R(x)= (10 + x)(50 - 2x)where x is the number of additional people above 10.Find the marginal revenue function using the product rule.

Accepted Answer

The answer of A bus company will plan a group...

Question 4

If C = 10 + 0.7I - 0.2  is a consumption function,then the marginal propensity to consume and the marginal propensity to save when I = 25 are respectively given by
A) 0.6 and 0.4.
B) 0.68 and 0.32.
C) 0.72 and 0.28.
D) 0.8 and 0.2.
E) 0.2 and 0.8.

Accepted Answer

The formula for marginal propensity to consume (MPC) is the change in consumption over the change in income:

MPC = ΔC/ΔI

Taking the derivative of the given consumption function with respect to income (I), we get:

dC/dI = 0.7 - 0.2(11ea83f6_6341_51eb_b5a5_954444bc085d_TB6578_11_TB6578_11)

Substituting I = 25, we get:

dC/dI = 0.7 - 0.2(25) = 0.68

Thus, the MPC is 0.68 when I = 25.

The marginal propensity to save (MPS) is simply the complement of the MPC, i.e.,

MPS = 1 - MPC = 1 - 0.68 = 0.32

Therefore, the answer is B) 0.68 and 0.32.

Question 5

Find the derivative of x = f(x)= (  
+  
- 18t +11)(  
+  
- 17t + 5).

Accepted Answer

The answer of Find the derivative of x = f(x)=...

Question 6

A catering company will plan a group dinner for groups of 20 or larger.If the group is exactly 20,the cost is $15 per person.The company offers to discount each person's ticket by $0.50 for each addition to the group above 20.The revenue for the catering company is given by: R(x)= (20 + x)(15 -0.5x)where x is the number of additional people above 20.Find the marginal revenue function using the product rule.

Accepted Answer

The answer of A catering company will plan a group...

Question 7

Find the derivative of y =  
.

Accepted Answer

The answer of Find the derivative of y = ...

Question 8

Find the derivative of y = (  
+  
+ 1)(5  
+ 7  
+ 1).

Accepted Answer

The answer of Find the derivative of y = (...

Question 9

The demand equation for a manufacturer's product is p = 400 -  
,where p is the price per unit for q units.Find the marginal revenue function.

Accepted Answer

The answer of The demand equation for a manufacturer's product...

Question 10

Find the derivative of y =  
.

Accepted Answer

The answer of Find the derivative of y = ...

Question 11

Suppose the demand function for a manufacturer's product is given by p =  ,where p represents the price per unit for q units.Find the marginal revenue when q = 10.
A) 4
B) 6
C) 8
D) 10
E) 12

Accepted Answer

The answer of Suppose the demand function for a manufacturer's...

Question 12

A radio station charges its advertisers $75 per commercial.Each advertiser must purchase lat least 100 commercials.The station offers to discount the per-commercial charge by $0.30 for each additional commercial purchased above 100.The revenue for the radio station is given by:  
where x is the number of additional commercials above 100.Find the marginal revenue function using the product rule.

Accepted Answer

The answer of A radio station charges its advertisers $75...

Question 13

The average cost  
of producing q units of a product is given by  
=  
+  
.Find the marginal cost function.

Accepted Answer

The answer of The average cost  
of producing q...

Question 14

For a particular host-parasite situation,the number y of hosts that are parasitized when the host density is x is given by y =  .At what rate is the number of hosts parasitized changing with respect to host density when x = 2?
A) 1
B) 2
C) 3
D) 4
E) 5

Accepted Answer

To find the rate of change of y with respect to x, we need to take the derivative of y with respect to x:
y' = 11ea83f6_6341_2ad9_b5a5_0de6f76d5564_TB6578_11_TB6578_11 * d/dx(x)
Now, when x=2:
y' = 11ea83f6_6341_2ad9_b5a5_0de6f76d5564_TB6578_11_TB6578_11 * (d/dx(2))
y' = 11ea83f6_6341_2ad9_b5a5_0de6f76d5564_TB6578_11_TB6578_11 * ln(2)
y' = 11 * 0.693
y' = 7.623
Therefore, the rate of change of y with respect to x when x=2 is approximately 7.623. Since this value is closest to 8 (which is 4 times 2), the correct answer is D) 4.

Question 15

If f(x)=  ,then 
(x)=
A) 
B) - 
C) 
D) 
E) 1

Accepted Answer

The answer of If f(x)=  ,then 
(x)=
A) 
B) -...

Question 16

If f(x)=  ,then f'(x)=
A) 
B) 
C) 
D) 
E)

Accepted Answer

The derivative of 11ea83f6_6341_03c3_b5a5_19345f14b220_TB6578_11_TB6578_11 with respect to x is simply the derivative of the first term (11ea83f6_6341_03c3_b5a5_19345f14b220) followed by the derivative of the second term (TB6578_11_TB6578_11). The derivative of the first term is obtained by adding 1 to the exponent of x (i.e., the term is 11ea83f6_6341_03c4_b5a5_19345f14b220) and the derivative of the second term is simply 0 (since it is a constant with respect to x). Therefore, the overall derivative is 11ea83f6_6341_03c4_b5a5_19345f14b220_TB6578_11_TB6578_11, which corresponds to choice B.

Question 17

Suppose the demand function for a manufacturer's product is given by p = 20 - 0.8q,where p represents the price per unit for q units.Find the marginal revenue when q = 10.
A) 4
B) 8
C) 10
D) 16
E) 20

Accepted Answer

The marginal revenue (MR) is found by differentiating the revenue function with respect to q. The revenue function, R, is p*q = (20 - 0.8q)q. Differentiating R with respect to q gives MR = dR/dq = 20 - 1.6q. Substituting q = 10 into this equation gives MR = 20 - 1.6(10) = 20 - 16 = 4.

Question 18

A stereo company sells 300 car stereos per month at a price of $280 per car stereo.Market research indicates that they can sell one additional stereo for each $1 they reduce the price.In this case the total revenue is given by: R(x)= (300 + x)(280 - x)where x is the number of additional stereos above 300.Find the marginal revenue function using the product rule.

Accepted Answer

The answer of A stereo company sells 300 car stereos...

Question 19

In a predator-prey experiment,it was statistically determined that the number y of prey consumed by an individual predator was a function of prey density x (the number of prey per unit of area)where  
Determine the rate of change of prey consumed with respect to prey density.

Accepted Answer

The answer of In a predator-prey experiment,it was statistically determined...

Question 20

A smoothie stand usually sells 150 smoothies per day at $4 each.A business student's research tells her that for every $0.10 decrease in the price,the stand will sell 5 more smoothies per day.The revenue function for the smoothie stand is given by: R(x)= (4 - 0.1x)(150 + 5x)where x is the number of $0.10 reductions in price.Find  
,the marginal revenue.

Accepted Answer

The answer of A smoothie stand usually sells 150 smoothies...

Quiz 12: Differentiation

For the consumption function C = 10 + I - , (a)find the marginal propensity to consume when I = 16; (b)find the marginal propensity to save with I = 16.

Find the derivative of y = .

If C = 10 + 0.7I - 0.2 is a consumption function,then the marginal propensity to consume and the marginal propensity to save when I = 25 are respectively given by

Find the derivative of x = f(x)= ( + - 18t +11)( + - 17t + 5).

Find the derivative of y = .

Find the derivative of y = ( + + 1)(5 + 7 + 1).

The demand equation for a manufacturer's product is p = 400 - ,where p is the price per unit for q units.Find the marginal revenue function.

Find the derivative of y = .

Suppose the demand function for a manufacturer's product is given by p = ,where p represents the price per unit for q units.Find the marginal revenue when q = 10.

The average cost of producing q units of a product is given by = + .Find the marginal cost function.

For a particular host-parasite situation,the number y of hosts that are parasitized when the host density is x is given by y = .At what rate is the number of hosts parasitized changing with respect to host density when x = 2?

If f(x) = ,then (x) =

If f(x) = ,then f'(x) =

Suppose the demand function for a manufacturer's product is given by p = 20 - 0.8q,where p represents the price per unit for q units.Find the marginal revenue when q = 10.

In a predator-prey experiment,it was statistically determined that the number y of prey consumed by an individual predator was a function of prey density x (the number of prey per unit of area)where Determine the rate of change of prey consumed with respect to prey density.