OE

You are given that each day the algae on the surface of a pond grows by 10% but then retracts 5% each night.

You are asked to compare the number of days it takes the algae to grow from 15% to 50% to the time it takes to grow from 50% to 100% of the pond surface.

Begin by calculating the growth each day:


(1 + .10)(1 - .05) = (1.10)(.95) = 1.045

Now set up the formula for geometric growth: start amount * growth rate^{time} = end amount

\(growth rate^{time}=\frac{end amount}{start amount }\) (it is essentially the percentage change formula)

At this point you can see that you don't actually need to calculate the number of days. Because the growth rate is the same for both Quantities you can see that whichever quantity is greater will result in a greater value for end amount

Therefore you only need to compare the ratios of the starting and ending amounts. start amount

\(\frac{50}{15}\) % \(\therefore \) \(\frac{100}{50}\) %


\(3.35>2\)

A is the answer