Answer:
(a)5347 Units
(b)[tex]N^{'}(a) =\dfrac{470}{a}[/tex]
(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)
[tex]\frac{d}{da}N(a) = \frac{d}{da}(2100+470ln(a))\\N^{'}(a) =\dfrac{470}{a}[/tex]
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
[tex]N^{'}(a) =\dfrac{470}{a}=0\\N^{'}(a) =470[/tex]
The maximum point of N(a)=470. The minimum point does not exist.
