Mr. Smith currently produces 45,000 bushels of potatoes a year.
He Can increase his harvest by an average rate of 3% annually.
How many years will it take until he can produce 50,000 bushels per year?
45000(1.03)^n = 50000
1.03^n = 1.1111...
n log 1.03 = log 1.111..
n = 3.5644..
about 3 1/2 years
To find out how many years it will take for Mr. Smith to produce 50,000 bushels per year, we can use a formula for compound interest, where:
Future Value (FV) = Present Value (PV) * (1 + r)^n
Here:
- FV is the future value of the production (50,000 bushels)
- PV is the present value of the production (45,000 bushels)
- r is the growth rate (3%, or 0.03)
- n is the number of years
We need to solve for n.
Rearranging the formula:
n = log(FV / PV) / log(1 + r)
Let's plug in the values and calculate:
n = log(50,000 / 45,000) / log(1 + 0.03)
Using a calculator, we get:
n ≈ log(1.1111) / log(1.03)
n ≈ 0.0465 / 0.0128
n ≈ 3.6328
Therefore, it will take approximately 3.6328 years (or around 4 years) for Mr. Smith to produce 50,000 bushels per year.