Answer to Question #151083 in Calculus for Angelo

Question #151083

A particular company has determined that when its weekly advertising expense is π‘₯ dollars,

then if 𝑆 dollars is its total weekly income from sales, 𝑆 = 4000 𝑙𝑛π‘₯.

(a) Determine the rate of change of sales income with respect to advertising expense when $800 is the weekly advertising budget.

(b) If the weekly advertising budget is increased to $950 dollars, what is the approximate increase in the total weekly income from sales?


1
Expert's answer
2020-12-21T19:11:22-0500

"a)S(x) = 4000\\ln{x}"

"\\text {rate of change of sales }S'(x)"

"S'(x)=(4000\\ln(x))'= \\frac{4000}{x}"

"S'(800)=\\frac{4000}{800}=5"


"\\text{(b) total weekly income from sales for advertising expense =800}"

"S_1= 4000\\ln(800)\\approx26738"

"\\text{for advertising expense =950}"

"S_1= 4000\\ln(950)\\approx27425"

"S_2-S_1=27425-26738 =687"


Answer:(a) 5 ; (b) 687








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