Question

algae is growing in a pond. after x days, the area of the pond covered in algae is 4^x square centimeters. how many times as large is the area covered in algae after 10 days than after 8 days? use the number pad to enter your answer in the box. blank times as large

Explanation:

Step1: Find the area after 10 days

The formula for the area is \( A(x)=4^x \). For \( x = 10 \), we have \( 4^{10} \).

Step2: Find the area after 8 days

For \( x = 8 \), the area is \( 4^{8} \).

Step3: Find the ratio of the two areas

To find how many times larger the area after 10 days is than after 8 days, we calculate \( \frac{4^{10}}{4^{8}} \). Using the exponent rule \( \frac{a^m}{a^n}=a^{m - n} \), we get \( 4^{10-8}=4^{2} \).

Step4: Calculate \( 4^{2} \)

\( 4^{2}=4\times4 = 16 \).

Answer:

16