Question

The height of a poplar tree in feet at age t years can be modeled by the function ℎ()=6+3(+1) . Use the model to predict the number of years when the height will exceed 17 feet.

Answer 1

Using the given function, it is found that it will take 38.12 years for the tree's height to exceed 17 feet.

When will the height exceed 17 feet?

The function that models the tree's height after t years is given by:

$h(t) = 6 + 3\ln{(t + 1)}$

It will be of 17 feet when h(t) = 17, hence:

$h(t) = 6 + 3\ln{(t + 1)}$

$17 = 6 + 3\ln{(t + 1)}$

$3\ln{(t + 1)} = 11$

$\ln{(t + 1)} = \frac{11}{3}$

$e^{\ln{(t + 1)}} = e^{\frac{11}{3}}$

$t + 1 = e^{\frac{11}{3}}$

$t = e^{\frac{11}{3}} - 1$

t = 38.12.

It will take 38.12 years for the tree's height to exceed 17 feet.

More can be learned about functions at https://brainly.com/question/25537936

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