Question

algae a lives in a warm, nutrient - rich pond and grows at a rate of 5% per year. algae b lives in a shaded, cooler lake and grows at a rate of 2% per year. \\(\frac{70}{r (growth rate)} = \text{doubling time}\\) using the rule of 70, which population will double first, and how long will it take? algae a, in 14 years algae b, in 35 years algae a, in 28 years

Explanation:

Step1: Calculate doubling time for Algae A

Using the formula $\frac{70}{r} = \text{Doubling Time}$, where $r = 5\%$ (or 5 in the formula, since we use the percentage value without the % sign). So, $\frac{70}{5} = 14$ years.

Step2: Calculate doubling time for Algae B

For Algae B, $r = 2\%$. Using the same formula, $\frac{70}{2} = 35$ years.

Step3: Compare the doubling times

Since 14 years (Algae A) is less than 35 years (Algae B), Algae A will double first in 14 years.

Answer:

algae A, in 14 years