Revenue
a small business assumes that the demand function for one of its new products can be modeled by p = cekx.
when p = $45, x = 1000 units, and when p = $40, x= 1200 units.
(a) solve for c and k in the model.
(b) find the values of x and p that will maximize the revenue for this product.

Step-by-step explanation:

Given that a  small business assumes that the demand function for one of its new products can be modeled by

Substitute  the given values for p and x to get two equations in c and k

Dividing on by other we get

Substitute value of k in any one equation

b) Revenue of the product is demand and price

i.e. R(x) = p*x =

Use Calculus derivative test to find max Revenue

R'(x) =

EquateI derivative to 0

1-0.000589x =0

x = 1698.037

When x = 1698 and p = 16.56469

hello,

b) 62.47% of the students are between 14 and 18 years old.

step-by-step explanation:

mean = 15 and standard deviation = 2

student between 14 to 18

formula used z-score

for age 14 , z score

using z-table , p(z> -0.5)=0.3085

for age 18 , z score

using z-table , p(z< 1.5)=0.9332

p(-0.5< z< 1.5)=0.9332-0.3085 = 0.6247

thus, 62.47% of the students are between 14 and 18 years old.

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step-by-step explanation: