Answer
a) $ -0.00001$ b) $10,536$ years c) $82$%
Work Step by Step
a) Given: $y=y_0e^{kt}$
Re-arrange the given equation as follows:.
Then, $0.99 y_0=y_0e^{1000k}$
Then $k=\dfrac{ \ln (0.99) }{1000} \approx -0.00001$
b) Given: $0.9=e^{-0.00001t}$
Re-arrange the given equation as follows:
Then $t=\dfrac{ \ln (0.9) }{-0.00001} \approx 10,536$ years
c) Given: $y=y_0e^{20,000k}$
Re-arrange the given equation as follows:.
Then, $y_0e^{-0.2}=y_0(0.82)$
Thus, $y=82$%
Hence, a) $ -0.00001$ b) $10,536$ years c) $82$%
