Question

Put the function P = 194(0.2)^t in the form
P = P0e^kt. (Round your answers to four decimal places.)

P0=
k=

Answer 1

\(\huge P=194(\frac{1}{5})^t=194\cdot 5^{-t} \rightarrow \frac{P}{194}=5^{-t} \)

\(\huge ln(\frac{P}{194})=ln(5^{-t}) \)
\(\huge ln(\frac{P}{194})=-t \cdot ln5 \)
\(\huge e^{ln(\frac{P}{194})}=e^{-t \cdot ln5} \)
\(\huge \frac{P}{194}=e^{(-ln5)(t)} \)
\(\huge P=\color {red}{194} \cdot e^{(\color {blue}{-ln5})(t)} \)
\(\huge P=\color {red}{P_0} \cdot e^{\color {blue}kt} \)

Answer 2

what is k?

Answer 3

is that a serious question?
match up the red and blue quantities....