Question

The amount of money invested in a certain account increases according to the function below, where y subscript 0 is the initial amount of the investment and y is the amount present at time t, in years.
y=y0e^0.0265t

Assuming no additional money is deposited or withdrawn, how many years will it take for the initial investment to double? Round your answer to the nearest tenth.

Answer 1

The time it will take the investment to double is 11.4 years

Exponential equations

Exponential equations are inverse of logarithmic equation. The standard exponential equation is expressed as y = ab^x

Given the equation that represents the amount of money invested in a certain account increase as shown;

y=y0e^0.0265t

If the initial investment doubles, the;

2y0 = y0e^0.0265t

2 = e^0.0265t

log2 = loge^0.0265t

0.3010 = 0.0265t

t = 0.3010/0.0265

t = 11.4 years

Hence the time it will take the investment to double is 11.4 years

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