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A certain city's population is 120,000 and decreases 1.4% per year for 15 years.
Is this exponential growth or decay? Growth
What is the rate of growth or decay?
What was the initial amount? 120000
What is the function?
What is the population after 10 years? Round to the nearest whole number.

Respuesta :

Answer:

  • Decay Problem.
  • Decay rate,  r = 0.014
  • Initial Amount =120,000
  • [tex]P(t)=120000(0.986)^t[/tex]
  • P(10)=104,220

Step-by-step explanation:

The exponential function for growth/decay is given as:

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

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:

[tex]P(t)=120000(1 - 0.014)^t\\P(t)=120000(0.986)^t[/tex]

When t=10 years

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

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