Question

1. (0 points) in 1965, latvia had a population of 2.27 million, and an exponential growth rate of 1.12%.

(a) find the exponential growth function.
ans: \\( p(t) = 2.27e^{0.0112t} \\)
(b) estimate the population in 1970. round your answer to the nearest tenth of a million.
ans: million

Explanation:

Step1: Identify the initial values

$$P_0 = 2.27, \quad k = 1.12\% = 0.0112$$

Step2: Write the growth function

$$P(t) = 2.27e^{0.0112t}$$

Step3: Calculate time elapsed

$$t = 1970 - 1965 = 5$$

Step4: Evaluate the population

$$P(5) = 2.27e^{0.0112 \times 5} \approx 2.4007$$

Answer:

(a) \(P(t) = 2.27e^{0.0112t}\)
(b) \(2.4\) million