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. $16.5\\,\text{cm}^2$
b. $14.7\\,\text{cm}^2$
c. $89.1\\,\text{cm}^2$
d. $125.3\\,\text{cm}^2$

Explanation:

Step1: Identify growth formula

This is exponential growth, formula: $A = P(1 + r)^t$
Where $P=11$ (initial area), $r=0.5$ (growth rate, since $1.5-1=0.5$), $t=6$ (months)

Step2: Substitute values

$A = 11\times(1.5)^6$

Step3: Calculate $(1.5)^6$

$1.5^2=2.25$, $1.5^3=2.25\times1.5=3.375$, $1.5^6=(3.375)^2=11.390625$

Step4: Compute final area

$A = 11\times11.390625 = 125.296875$

Answer:

D. $125.3\ \text{cm}^2$