this is a economic task Alg 1b

Question

Mrs. Franklin uses the formula A=-10m^2+60m+300 to predict how the amount an average customer spends at her store will change over time, where A is the amount in $, and m is the number of months after the customers initial purchase.

a.What is the maximum the average customer will spend according to this model and after how many months will it occur?

b.The model predicts  that the amount the average customer spends will eventually fall to 0.00. After how many months is this predicted to happen?

 

Answer 1

a.To find the maximum of (-10m²+60m+300) you differentiate A(m) with respect to m which gives dA/dm=-20m*(m-3) and set it equal to 0 dA/dm=0 at m=3 months. Putting this value in A(3)=$390 which id the maximum amount spent.

 

b.A=0 at m=3+√39 =9.25 months the other root is negative and has no physical meaning.

 

Jim