The sales of lawn mowers t years after a particular model is introduced is given by the function y = 5500 ln(9t + 4), where y is the number of mowers sold. How many mowers will be sold 3 years after a model is introduced? Round the answer to the nearest whole number.

Answers

Answer 1

Given:

The function is:

[tex]y=5500\ln (9t+4)[/tex]

Where y is the sales of lawn mowers t years after a particular model is introduced.

To find:

How many mowers will be sold 3 years after a model is introduced?

Solution:

We have,

[tex]y=5500\ln (9t+4)[/tex]

Substituting [tex]t=3[/tex], we get

[tex]y=5500\ln (9(3)+4)[/tex]

[tex]y=5500\ln (27+4)[/tex]

[tex]y=5500\ln (31)[/tex]

On substituting the approximate value of ln(31), we get

[tex]y=5500\times 3.433987[/tex]

[tex]y=18886.9285[/tex]

[tex]y\approx 18887[/tex]

Therefore, the 18887 mowers will be sold 3 years after a model is introduced.


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