Question

of exponential functions (includes 5.1b) question completed: 22 of 28 my score: 22/28 pts (78.57%) the population of a midwest industrial town decreased from 214,000 to 210,000 in just 2 years. assuming uninhibited exponential decay, what will the population be after an additional 5 years? the population will be about \square. (do not round until the final answer. then round to the nearest whole number as needed.)

Explanation:

Step1: Define decay formula

Exponential decay: $P(t) = P_0 e^{kt}$, $P_0=214000$, $t=2$ when $P=210000$.

Step2: Solve for k

Substitute: $210000 = 214000 e^{2k}$ → $\frac{210000}{214000} = e^{2k}$ → $\ln(\frac{210}{214}) = 2k$ → $k=\frac{1}{2}\ln(\frac{210}{214})≈-0.00944$.

Step3: Calculate total time

Total time: $2+5=7$ years.

Step4: Compute population at t=7

$P(7)=214000 e^{-0.00944×7}≈214000×0.935≈200090$.

Answer:

200090