Question

A model for​ consumers' response to advertising is given by the equation N(a)=2100+470ln(a) Where​ N(a) is the number of units​ sold, a is the amount spent on​ advertising, in thousands of​ dollars, & a≥1.

Answer 1

Answer:

(a)5347 Units

(b)$N^{'}(a) =\dfrac{470}{a}$

(c)The maximum point of N(a)=470. The minimum point does not exist.

Step-by-step explanation:

a) How many units were sold after spending $1,000 on advertising?

N(a)=2100+470ln(a)

N(1000)=2100+470ln(1000)

           =2100+3246.6

           =5346.6 ≈ 5347 Units

b) We are required to find the derivative of N(a)

N(a)=2100+470ln(a)

$\frac{d}{da}N(a) = \frac{d}{da}(2100+470ln(a))\\N^{'}(a) =\dfrac{470}{a}$

c) Find the maximum and minimum values of  N(a) if they exist.

The maximum and/or minimum value of N(a) is the point at which the slope or derivative of N(a)=0.

Given that

$N^{'}(a) =\dfrac{470}{a}=0\\N^{'}(a) =470$

The maximum point of N(a)=470. The minimum point does not exist.