The function f (x) = 57.8 (1.02) x gives the approximate number of passenger cars, in millions, in the United States x years after 1960. Using this model, in about what year will the number of passenger cars reach 200 million

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Mathematics

Logan Schmidt

1 September, 15:24

The function f (x) = 57.8 (1.02) x gives the approximate number of passenger cars, in millions, in the United States x years after 1960. Using this model, in about what year will the number of passenger cars reach 200 million

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Ella Cameron · Answer 1

Assume this is f (x) = 57.8 (1.02) ˣ. This is a 2% increase each year.

When f (x) = 200, 57.8 (1.02) ˣ=200, (1.02) ˣ=200/57.8

Taking logs, xlog (1.02) = log (200/57.8), x = log (200/57.8) / log (1.02) = 62.685.

Add 1960 to 62.685=2023 approx.