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
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
Solution 1
To solve this problem, we need to use the formula for compound interest, which is also applicable to population growth and decay problems. The formula is:
A = P(1 + r/n)^(nt)
where:
- A is the amount of the final quantity (the number of infected plants after 8 years in this case)
- P is the principal amount (the initial quantity, which is 458 infected plants)
- r is the annual growth rate (8% or 0.08 in decimal form)
- n is the number of times the interest is compounded per year (since the disease spreads annually, n = 1)
- t is the time the money is invested for in years (8 years in this case)
Substituting the given values into the formula, we get:
A = 458(1 + 0.08/1)^(1*8) A = 458(1 + 0.08)^8 A = 458(1.08)^8
Now, calculate the value of A to find out how many plants will be infected in 8 years. If necessary, round your answer to the nearest whole number.
Solution 2
To solve this problem, we need to use the formula for compound interest, which is also applicable to population growth and decay problems. The formula is:
A = P(1 + r/n)^(nt)
where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (in decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for in years.
In this case, we are looking for the number of banana plants infected after 8 years. So, we have:
- P = 458 (the initial number of infected plants)
- r = 0.08 (the rate of spread of the disease per year, in decimal)
- n = 1 (the number of times the disease spreads per year)
- t = 8 (the number of years)
Substituting these values into the formula, we get:
A = 458(1 + 0.08/1)^(1*8) A = 458(1 + 0.08)^8 A = 458(1.08)^8
Now, calculate the value of A to find the number of infected plants after 8 years. If necessary, round your answer to the nearest whole number.
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