Answer:
A. 11.55
Explanation:
Given:
[tex]A(t)=A_oe^{rt},t=\text{days}[/tex]
• If the initial amount of substance, A0=1
,
• Then, if after time t, the amount doubles, then A(t)=2
,
• r=6% =0.06
Substitute all these values into the equation.
[tex]\begin{gathered} 2=1e^{0.06t} \\ \implies e^{0.06t}=2 \end{gathered}[/tex]
Next, take the natural logarithm of both sides:
[tex]\begin{gathered} \ln (e^{0.06t})=\ln (2) \\ 0.06t=\ln (2) \\ \implies t=\frac{\ln (2)}{0.06} \\ t=11.55\text{ days} \end{gathered}[/tex]
The doubling time (at a rate of 6%) is 11.55 days.
