The correct answer is:
46.6 days
Explanation:
The general form for exponential growth is
[tex] A=p(1+r)^t [/tex], where A is the total amount, p is the initial amount, r is the percent of growth, and t is the amount of time (in this case, days).
We do not know the initial amount, the total amount, or the amount of time. We do know that r, the percent of growth, is 1.5%; 1.5% = 1.5/100 = 0.015:
[tex] A=p(1+0.015)^t [/tex]
We also know we want the total amount, A, to be twice that of the initial amount, p:
[tex] 2p = p(1+0.015)^t
\\
2p=p(1.015)^t [/tex]
Divide both sides by p:
[tex] \frac{2p}{p}=\frac{p(1.015)^t}{p}
\\
\\ 2=1.015^t [/tex]
Using logarithms to solve this,
[tex] \log_{1.015}(2)=t
\\
\\46.6=t [/tex]
