In a greenhouse, the estimated number of flowering plants increased from 4100 in January 2024 to 4980 in June 2024. The number increased by $c\%$ every month. Find the value of $c$. Answer c = ...

1. Set up the compound percentage increase equation

From January 2024 to June 2024, there are $5$ monthly increases.

If the number increases by $c\%$ each month, the monthly multiplier is $1+\dfrac{c}{100}$.

$4100\left(1+\frac{c}{100}\right)^5=4980$

2. Isolate the monthly growth multiplier

$\left(1+\frac{c}{100}\right)^5=\frac{4980}{4100}$

$1+\frac{c}{100}=\left(\frac{4980}{4100}\right)^{\frac15}$

3. Calculate the percentage increase per month

$c=100\left[\left(\frac{4980}{4100}\right)^{\frac15}-1\right]$

$c\approx 3.977\ldots$

To 2 significant figures,

$c=4.0$