Question

1. (10 points) in 1965, the population of the dominican republic had an exponential growth rate of \\(3.16\\%\\). how many years until the population doubles? round your answer to the nearest tenth of a year.

ans: years

1. (20 points) you have 6.9 pounds of einsteinium-252, which has an exponential decay rate of \\(0.15\\%\\) per day.

(a) find the exponential decay function.

Explanation:

Step1: Identify the doubling time formula

$$T = \frac{\ln(2)}{r}$$

Step2: Substitute the growth rate

$$T = \frac{\ln(2)}{0.0316}$$

Step3: Calculate the doubling time

$$T \approx 21.935 \approx 21.9\text{ years}$$

Step4: Identify the decay function formula

$$A(t) = A_0 e^{-kt}$$

Step5: Substitute the given values

$$A(t) = 6.9e^{-0.0015t}$$

Answer:

1. 21.9 years
2. (a) \(A(t) = 6.9e^{-0.0015t}\)