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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 5 years after a model is introduced? Round the answer to the nearest whole number.

Verified Answer :

\(y=5500 \ln{(9t+4)} \\t=5 \\y=5500 \ln{(9 \times 5+4)} \\y=5500 \ln{49} \\y=5500 \times \ln{7^2} \\y=5500 \times 2 \ln{7} \\y=11000 \times 1.95 \\y=21450\)

Answer:

21450 mowers have been sold in 5 years.

Step-by-step explanation:

The function for the sales of lawn mowers t years is given by

y = 5500 ln(9t + 4)

where t is in years and y represents number of mowers.

We have to calculate the sales of mowers after 5 years.

So we will use the function to calculate the numbers by putting t = 5

y = 5500×ln(9×5 + 4) = 5500×ln(45+4) = 5500×ln(49) = 5500×ln(7²)

y = 5500×[2ln(7)] = 5500×2×(1.95) = 21450

Therefore answer is 21450 mowers have been sold

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