Question

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.

Answer 1

Given:

The function is:

$y=5500\ln (9t+4)$

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,

$y=5500\ln (9t+4)$

Substituting $t=3$, we get

$y=5500\ln (9(3)+4)$

$y=5500\ln (27+4)$

$y=5500\ln (31)$

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

$y=5500\times 3.433987$

$y=18886.9285$

$y\approx 18887$

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