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 \( A \) 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 calculate \( A = 458(1 + 0.08)^8 \).

Step3: Calculate the exponent first

\( (1 + 0.08)^8 = 1.08^8 \). Using a calculator, \( 1.08^8 \approx 1.85093 \).

Step4: Multiply by the initial amount

\( A = 458 \times 1.85093 \approx 458 \times 1.85093 \approx 847.73 \). Rounding to the nearest whole number gives 848.

Answer:

848