Question

select the correct answer. paul is gathering data about moss growth in a local forest. he measured an area of 11 square centimeters on one particular tree and will come back in 6 months to measure the growth of the moss. if the area covered by moss multiplies by one and a half times each month, approximately how much area will the moss cover when paul returns?
a. 125.3 cm²
b. 99.1 cm²
c. 14.7 cm²
d. 16.5 cm²

Explanation:

Step1: Identify the growth - formula

This is a compound - growth problem. The formula for compound growth is $A = P(1 + r)^n$, where $P$ is the initial amount, $r$ is the growth rate per period, and $n$ is the number of periods. Here, $P = 11$ square centimeters, $r=0.5$ (since it multiplies by one - and - a - half times, so the growth rate is $1.5−1 = 0.5$), and $n = 6$.

Step2: Substitute the values into the formula

$A=11\times(1 + 0.5)^6=11\times1.5^6$.

Step3: Calculate $1.5^6$

$1.5^6=1.5\times1.5\times1.5\times1.5\times1.5\times1.5 = 11.390625$.

Step4: Calculate the final area

$A = 11\times11.390625=125.296875\approx125.3$ square centimeters.

Answer:

A. $125.3\ cm^{2}$