Question

a blight is spreading in a banana plantation. currently, 458 banana plants are infected. if the disease is spreading at a rate of 8% each year, how many plants will be infected in 8 years? if necessary, round your answer to the nearest whole number. blank banana plants submit

Explanation:

Step1: Identify the formula for exponential growth

The formula for exponential growth is $A = P(1 + r)^t$, where $A$ is the final amount, $P$ is the initial amount, $r$ is the annual growth rate (as a decimal), and $t$ is the time in years.

Step2: Plug in the given values

Here, $P = 458$, $r = 0.08$ (since 8% = 0.08), and $t = 8$. So we have $A = 458(1 + 0.08)^8$.

Step3: Calculate the value inside the parentheses first

$1 + 0.08 = 1.08$.

Step4: Raise 1.08 to the power of 8

$1.08^8 \approx 1.85093021$.

Step5: Multiply by the initial amount

$A = 458 \times 1.85093021 \approx 847.726036$.

Step6: Round to the nearest whole number

Rounding 847.726036 to the nearest whole number gives 848.

Answer:

848