Question

1. a trees height is modeled by $h(t) = 4 \times (1.1)^t$, where $h(t)$ is in feet and $t$ is in years. after 5 years, how tall will the tree be?

a. 4 feet
b. 6.44 feet
c. 7.65 feet
d. 6 feet

Explanation:

Step1: Identify the value of t

We know that \( t = 5 \) years (since we want to find the height after 5 years).

Step2: Substitute t into the function

The function is \( H(t)=4\times(1.1)^{t} \). Substitute \( t = 5 \) into it:
\( H(5)=4\times(1.1)^{5} \)
First, calculate \( (1.1)^{5} \). \( (1.1)^{5}=1.1\times1.1\times1.1\times1.1\times1.1 = 1.61051 \)
Then, multiply by 4: \( H(5)=4\times1.61051 = 6.44204\approx6.44 \)

Answer:

b. 6.44 feet