A corn farmer produces 40,000 bushels of corn in her first year of farming. Due to improved farming techniques, she increases the production by 5% each year. How many total bushels of corn did she produce in her first 4 years of farming? Round your answer to the nearest whole number.(1 point) Responses 148,395 bushels 148,395 bushels 221,025 bushels 221,025 bushels 161,204 bushels 161,204 bushels 172,405 bushels
Using the formula for calculating future value with a constant growth rate:
FV = PV * (1 + r)^n
Where:
FV = future value
PV = present value (initial production in the first year)
r = growth rate (5% or 0.05)
n = number of years
For the first 4 years, we calculate the total production:
Year 1: 40,000 bushels
Year 2: 40,000 * (1 + 0.05) = 42,000 bushels
Year 3: 42,000 * (1 + 0.05) = 44,100 bushels
Year 4: 44,100 * (1 + 0.05) = 46,305 bushels
Adding all the productions together:
40,000 + 42,000 + 44,100 + 46,305 = 172,405 bushels
Therefore, the total bushels of corn she produced in her first 4 years of farming is 172,405 bushels. The closest answer choice is:
172,405 bushels