Your question is missing formula for m which is given as;
formula for [tex]m= \frac{p^3}{90}[/tex]
Answer:
a.the inverse of the function is [tex]p=\sqrt[3]{90m}[/tex].
b.p=12 (thousands)
Step-by-step explanation:
Given Data:
Formula for [tex]m= \frac{p^3}{90}[/tex] , where m is the total number of months it takes to produce p tennis rackets (in thousands).
Required:
a. Find the inverse of the function.
b. How many tennis rackets will be produced in 20 months? Round your answer to the nearest whole tennis racket.
Solution:
a.Inverse of the function:
[tex]m= \frac{p^3}{90}\\\\multiply\ both\ sides\ by\ 90\ we\ get\\p^3=m*90\\\\p^3=90m\\\\taking\ cube\ root\ we\ get\\\\p=\sqrt[3]{90m}[/tex]
the inverse of the function is [tex]p=\sqrt[3]{90m}[/tex]........Eq1
b. How many tennis rackets will be produced in 20 months?
put m=20 in Eq1, we get
[tex]p=\sqrt[3]{90*20}\\\\p=\sqrt[3]{1800}\\\\p=12.16[/tex]
If we round the answer to nearest whole tennis racket we get p=12 (thousands)
thus, in 20 moths 12 (thousands) tennis rackets will be produced
