QUESTION $20 \cdot 1$ POINT A population of kangaroos is growing at a rate of $2 \%$ per year, compounded continuously. If the growth rate continues, how many years will it take for the size of the population to reach $150 \%$ of its current size according to the exponential growth function? Round your answer up to the nearest whole number, and do not include units. Provide your answer below: FEEDBACK

Step 1 ：The problem is asking for the time it will take for a population to grow to 150% of its current size, given a continuous growth rate of 2% per year. This is a problem of exponential growth, and we can use the formula for continuous compound interest to solve it.

Step 2 ：The formula for continuous compound interest is: \(A = P \cdot e^{rt}\) where: \(A\) is the final amount (in this case, 150% of the initial population), \(P\) is the initial amount (in this case, the initial population), \(r\) is the rate of growth (in this case, 2% per year, or 0.02 when expressed as a decimal), \(t\) is the time (in years), and \(e\) is the base of the natural logarithm (approximately 2.71828).

Step 3 ：We can rearrange this formula to solve for \(t\): \(t = \frac{ln(A/P)}{r}\)

Step 4 ：Given that \(P = 1\), \(A = 1.5\), and \(r = 0.02\), we can plug in these values and solve for \(t\).

Step 5 ：Doing so, we find that \(t = 21\).

Step 6 ：Final Answer: The population of kangaroos will reach 150% of its current size in \(\boxed{21}\) years.