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The population of a city was 136 thousand in 1992. The exponential growth rate was 1.7% per year.a) Find the exponential growth function in terms of t, where t is the number of years since 1992.P(t) = 136,000 e 0.0177b) Predict the population in 2005, to the nearest thousand.(Round to the nearest thousand as needed.)

Respuesta :

We are given that a city has a population of 136000 in 1992 and a growth rate of 1.7% per year.

Part a) An exponential function that models the exponential growth is given by:

[tex]P=P_0e^{rt}[/tex]

Where

[tex]\begin{gathered} P_0=\text{ initial population} \\ r=\text{ growth rate in decimal form} \\ t=\text{ time} \end{gathered}[/tex]

The growth rate in decimal form is the following:

[tex]r=\frac{1.7}{100}=0.017[/tex]

Now we substitute the values and we get:

[tex]P=136000e^{0.017t}[/tex]

Part b) For the year 2005 there are 13 years, therefore, we substitute in the equation the values t = 13:

[tex]P=136000e^{(0.017)(13)}[/tex]

Solving the operations we get:

[tex]P=169636\approx170000[/tex]

Therefore, the population in 2005 is approximately 170000.

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