Question

A certain city's population is 120,000 and decreases 1.4% per year for 15 years.

Answer 1

Answer:

• Decay Problem.

• Decay rate,  r = 0.014
• Initial Amount =120,000

• $P(t)=120000(0.986)^t$
• P(10)=104,220

Step-by-step explanation:

The exponential function for growth/decay is given as:

$P(t)=P_0(1 \pm r)^t, where:\\P_0 is the Initial Population\\r is the growth/decay rate\\t is time$

In this problem:

The city's initial population is 120,000 and it decreases by 1.4% per year.

• Since the population decreases, it is a Decay Problem.

• Decay rate, r=1.4% =0.014
• Initial Amount =120,000

Therefore, the function is:

$P(t)=120000(1 - 0.014)^t\\P(t)=120000(0.986)^t$

When t=10 years

$P(10)=120000(0.986)^10\\=104219.8\\\approx 104220 (to the nearest whole number)$