Question

an investment triples every 12 years.
what is the annual interest rate (compounded continuously)?
round to the ten - thousandths place.
r=
0.0916
question 4
1 pts
a bacteria population doubles every 3 hours.
if 500 bacteria are present initially, how many after 12 hours?

Explanation:

Step1: Determine the number of doubling periods

The bacteria population doubles every 3 hours. For a time period of 12 hours, the number of doubling periods \(n=\frac{12}{3} = 4\).

Step2: Use the formula for exponential growth (doubling)

The formula for a quantity that doubles is \(P = P_0\times2^n\), where \(P_0\) is the initial population and \(n\) is the number of doubling periods. Given \(P_0 = 500\) and \(n = 4\), we substitute into the formula: \(P=500\times2^4\).
Calculate \(2^4=16\), then \(P = 500\times16\).

Step3: Compute the final population

\(P=500\times16 = 8000\).

Answer:

8000