RIDGE Assignment $2 \mathrm{~A} .5$ Assignment 2 A. 5 account after t years, $P=$ principal invested, and $r=$ the annual interest rate, how many years, to the nearest tenth, will it double? b) to triple? c) to quadruple? 2. The population of Allenwood is 158,000 and is increasing at an annual rate of $8.25 \%$. This situation is modeled by the e $P(t)$ represents the total population and $t$ represents the number of years from now. a) How many years; to the nearest hundredth, will it take for the original population to double? b) to triple? c) to quadruple?

Step 1 ：\(A = P(1 + r)^t\)

Step 2 ：\(2P = P(1 + 0.5)^t\)

Step 3 ：\(t \approx 1.7\) years to double

Step 4 ：\(3P = P(1 + 0.5)^t\)

Step 5 ：\(t \approx 2.7\) years to triple

Step 6 ：\(4P = P(1 + 0.5)^t\)

Step 7 ：\(t \approx 3.4\) years to quadruple

Step 8 ：\(P(t) = P_0(1 + r)^t\)

Step 9 ：\(2(158000) = 158000(1 + 0.0825)^t\)

Step 10 ：\(t \approx 8.7\) years to double population

Step 11 ：\(3(158000) = 158000(1 + 0.0825)^t\)

Step 12 ：\(t \approx 13.9\) years to triple population

Step 13 ：\(4(158000) = 158000(1 + 0.0825)^t\)

Step 14 ：\(t \approx 17.5\) years to quadruple population

Step 15 ：\(\boxed{1.7}\) years for principal to double

Step 16 ：\(\boxed{2.7}\) years for principal to triple

Step 17 ：\(\boxed{3.4}\) years for principal to quadruple

Step 18 ：\(\boxed{8.7}\) years for Allenwood population to double

Step 19 ：\(\boxed{13.9}\) years for Allenwood population to triple

Step 20 ：\(\boxed{17.5}\) years for Allenwood population to quadruple