Question

Find the candle company's sales in 2000. (Round your answer to two decimal places)

Answer 1

The model for the sales is
`S = 0.264t^2 + 597.2091\ln(t) - 1076.89` and the candle company's sales in 2000 is $324.63

Finding a model for the sales

From the question, we have the following parameters that can be used in our computation:

`(ds)/(dt) = 0.528t + (597.2091)/(t)`

Integrate the function

So, we have

`S = (0.528t^2)/(2) + 597.2091\ln(t) + c`

`S = 0.264t^2 + 597.2091\ln(t) + c`

We have that

The sales in 1999 is $256.7 million

So, we have

`0.264 * 9^2 + 597.2091\ln(9) + c = 256.7`

1333.6 + c = 256.7

So, we have

c = 256.7 - 1333.6

c = -1076.89

So, we have

`S = 0.264t^2 + 597.2091\ln(t) - 1076.89`

In 2000, we have t = 10

So:

`S = 0.264 * 10^2 + 597.2091\ln(10) - 1076.89`

S = 324.63

Hence, the sales is 324.63