an investment triples every 12 years.\nwhat is the annual interest rate (compounded continuously)?\nround to…

an investment triples every 12 years.\nwhat is the annual interest rate (compounded continuously)?\nround to the ten - thousandths place.\nr=\n0.0916\nquestion 4\n1 pts\na bacteria population doubles every 3 hours.\nif 500 bacteria are present initially, how many after 12 hours?

an investment triples every 12 years.\nwhat is the annual interest rate (compounded continuously)?\nround to the ten - thousandths place.\nr=\n0.0916\nquestion 4\n1 pts\na bacteria population doubles every 3 hours.\nif 500 bacteria are present initially, how many after 12 hours?

Answer

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