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write a exponential function to model the situation then find the value of your function after the given amount of time the population of a town is 18,000 and is decreasing at the rate of 2% per year : 6 years

User Shaz
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1 Answer

16 votes
16 votes

Step-by-step explanation:

The exponential function that models this situation is:


n(t)=n_0(1-r)^t

Where n(t) is the amount we want to model the decay, n0 is the initial amout, r is the rate of decay and t is the time in years.

For this particular problem we have n0 = 18,000, r = 0.02 and we have to find n(6)


\begin{gathered} n(t)=18,000(1-0.02)^t \\ n(t)=18,000*0.98^t \end{gathered}

When t = 6:


n(6)=18,000*0.98^6=15,945.16286

Answers:

• Function:


n(t)=18,000*0.98^t

Population after 6 years: 15,945

User Nuibb
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