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. banana plants submit

Explanation:

Step1: Identify the formula for exponential growth

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

Step2: Convert the growth rate to a decimal

The growth rate is 8%, so $r = \frac{8}{100} = 0.08$.

Step3: Substitute the values into the formula

We have $P = 458$, $r = 0.08$, and $t = 8$. Substituting these into the formula gives $A = 458(1 + 0.08)^8$.

Step4: Calculate $(1 + 0.08)^8$

First, calculate $1 + 0.08 = 1.08$. Then, $1.08^8 \approx 1.85093021$.

Step5: Multiply by the initial amount

Multiply $458$ by $1.85093021$: $A = 458 \times 1.85093021 \approx 847.726036$.

Step6: Round to the nearest whole number

Rounding $847.726036$ to the nearest whole number gives $848$.

Answer:

848