Answer
a) $\approx 8$ years b) $\approx 32.02$ years
Work Step by Step
a) Given: $y=1000$ and $y_0=10,000$
The exponential growth can be written as: $y=y_0e^{kt}$ ...(1)
Then, $1,000=10,000 e^{(\ln 0.75)t}$
This implies that $t=\dfrac{\ln (0.1)}{\ln (0.75)}$
or, $t \approx 8$ years
b) Given: $y=1$ and $y_0=10,000$
The exponential growth can be written as: $y=y_0e^{kt}$ ...(1)
Then, $1=10,000 e^{(\ln 0.75)t}$
This implies that $t=\dfrac{\ln (0.0001)}{\ln (0.75)}$
or, $t \approx 32.02$ years
Hence, a) $\approx 8$ years b) $\approx 32.02$ years