Question

a new tennis club opened with 25 members. the membership of the club can be approximated by the formula $c = 25(1.2)^m$ where $m$ represents the number of months and $c$ represents the total club membership. after how many months will the club have about 43 members?
a 2
b 3
c 4
d 5

Explanation:

Step1: Set up equation

Set $43 = 25(1.2)^m$

Step2: Isolate exponential term

Divide both sides by 25: $\frac{43}{25} = (1.2)^m$, so $1.72 = (1.2)^m$

Step3: Solve for m with logs

Take natural log of both sides: $\ln(1.72) = m\cdot\ln(1.2)$
$m = \frac{\ln(1.72)}{\ln(1.2)} \approx \frac{0.5423}{0.1823} \approx 2.975$

Step4: Round to nearest whole month

The value is approximately 3 months.

Answer:

B 3