Question

The annual profit P(t) of the Enviro Company, in thousands of dollars, is
given by
P(t) = 2+3 – 152++ 3400t + 30
where t is the number of years since 1960, the first year that the company
showed a profit.
Fill in the blanks below. All answers should be rounded to the nearest dollar.
Do not use commas in your solution.

The profit in 1960 was____ dollars.

Answer 1

Answer:

The profit in 1960 (i.e. year 1) was 3280 dollars

Step-by-step explanation:

Given

$P(t) = 2t^3 - 152t^2 + 3400t + 30$

Where

t = years since 1960 (the first year)

Required

Determine the profit in 1960

Since the first year is 1960, then $t =1$

To get the profit, we simply substitute 1 for t in $P(t) = 2t^3 - 152t^2 + 3400t + 30$

$P(t) = 2t^3 - 152t^2 + 3400t + 30$ becomes

$P(1) = 2(1)^3 - 152(1)^2 + 3400(1) + 30$

$P(1) = 2*1 - 152*1 + 3400*1 + 30$

$P(1) = 2- 152 + 3400 + 30$

$P(1) = 3280$

Hence, the profit in 1960 (i.e. year 1) was 3280 dollars