a blight is spreading in a banana plantation. currently, 458 banana plants are infected. if the disease is…

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

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

Answer

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