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

To calculate the profit for the Enviro Company in 1960, substitute t = 0 into the profit function, assuming a typo clearance in the formula the profit was 30,000 dollars.

Step-by-step explanation:

The profit in 1960 for the Enviro Company can be calculated by substituting t = 0 into the given profit function P(t), as t represents the number of years since 1960. However, there seems to be a typo in the function provided. Assuming the correct profit function should be P(t) = 2t^3 + 3400t + 30, we find that the profit in 1960 when t = 0 is P(0) = 2(0)^3 + 3400(0) + 30 = 30 thousand dollars. Therefore, the profit in 1960 was 30,000 dollars.

Answer 2

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