Answer
a) $\approx 8$ years b) $\approx 32.02$ years
Work Step by Step
a) Consider the exponential growth as: $y=y_0e^{kt}$
As we are given that $y=1000$ and $y_0=10,000$
Then, we get $1,000=10,000 e^{(\ln 0.75)t}$
or, $t=\dfrac{\ln (0.1)}{\ln (0.75)}$
Thus, $t \approx 8$ years
b) Consider the exponential growth as: $y=y_0e^{kt}$
As we are given that $y=1$ and $y_0=10,000$
Thus, we have $(1)=(10,000) e^{(\ln 0.75)t}$
or, $t=\dfrac{\ln (0.0001)}{\ln (0.75)}$
Thus, $t \approx 32.02$ years
