mr thompson plans to invest $7,500 in a savings account that earns 2.75% simple nnual interest. If he makes no other deposits or
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Answer:
35.4 years
Step-by-step explanation:
The annual consumption (in billions of units) is described by the exponential function ...
f(t) = 45.5·1.026^t
The accumulated consumption is described by the integral ...
We want to find t such that the value of this integral is 2625, the estimated oil reserves.
2625 = 45.5/ln(1.026)·(1.026^t -1)
2625·ln(1.026)/45.5 +1 = 1.026^t ≈ 1.480832 +1 = 1.026^t
Taking natural logs, we have ...
ln(2.480832) = t·ln(1.026)
t ≈ ln(2.480832)/ln(1.026) ≈ 35.398
After about 35.4 years, the oil reserves will run out.
The function will show exponential decay if one of the following is true
- the base is less than 1 and the exponent is positive
- the base is greater than 1 and the exponent is negative
The function that meets the requirement for exponential decay is ...