The population of a particular city is given by the function P(t) = 82,100(1.02)^t, where t is the time in years and P(t) is the population after t years. What is the current population, the percentage growth rate, and the population size (rounded to the nearest whole person) after 15 years?
Hint: Percentage Growth Rate = r ⋅ 100 in A = A0(1 + r)^t
A.) 82,000, 2% semiannually,110,658
B.) 82,100,10.2% annually, 352,425
C.) 82,100, 2% annually, 110,496
D.)82,100,20% semiannually, 985,200
+2498 P(t) = 82,100(1.02)^t
1.t is the time in years
2.P(t) is the population after t years
3. 100%=1 102-100=2% so the interest rate is 2 %
102%=1.02
4. after 15 year just put in term s of 't' (wich is represent the years) 15 :
\(82,100 \times(1.02)^{15}=110495.7905764110395150475397398528=110.496\text{ (aprox.)} \)
+2498 P(t) = 82,100(1.02)^t
1.t is the time in years
2.P(t) is the population after t years
3. 100%=1 102-100=2% so the interest rate is 2 %
102%=1.02
4. after 15 year just put in term s of 't' (wich is represent the years) 15 :
\(82,100 \times(1.02)^{15}=110495.7905764110395150475397398528=110.496\text{ (aprox.)} \)
