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?
\(\boxed{17.5}\) years for Allenwood population 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