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

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 (in decimal), and $t$ is the time in years.

Step2: Convert the growth rate to decimal

The growth rate $r$ is 8%, which is $0.08$ in decimal.

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, $1.08^8 \approx 1.85093$.

Step5: Calculate the final amount $A$

Multiply $458$ by $1.85093$: $A = 458 \times 1.85093 \approx 847.726$.

Step6: Round to the nearest whole number

Rounding $847.726$ to the nearest whole number gives $848$.

Answer:

848