Question

The height of a poplar tree in feet at age t years can be modeled by the function h(t)=6+3ln(t+1) . use the model to predict the number of years when the height will exceed 18 feet.

Answer 1

The function h(t)=6+3ln(t+1) is a logarithmic function

The height of the tree will exceed 18 feet after 53.6 years

How to determine the number of years?

The function is given as:

h(t)=6+3ln(t+1)

When the height is 18 feet, we have:

6+3ln(t+1) = 18

Subtract 6 from both sides

3ln(t+1) = 12

Divide both sides by 3

ln(t+1) = 4

Take the exponent of both sides

t + 1 = e^4

Evaluate the exponent

t + 1 = 54.6

Subtract 1 from both sides

t = 53.6

This means that the height of the tree will exceed 18 feet after 53.6 years

Read more about logarithmic functions at:

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