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a city with a population of 28,405 people is predicted to grow exponentially, at an annual rate of 2.4% which of the following equations should be should be used to find the population of the city 5 years from now?
A.p(5)=28,405(1+0.024)^5
B.p(5)=28,405(1-0.024)^5
C.p(5)=28,405(1+5)^2.4
D.p(5)=28,405(1+0.24)^5

Respuesta :

Answer:

The population of city after 5 years is 28,405 [tex](1+0.024)^{\textrm 5}[/tex]  .

Step-by-step explanation:

Given as :

The initial population of city = p = 28,405

The rate of grow of population = r = 2.4% annual

The time period for population = t = 5 years

Let The population of city after 5 years = P

Now, According to question

The Population of city after n years = initial population × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]

Or, The Population of city after 5 years = initial population × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]

Or, P = p × [tex](1+\dfrac{\textrm r}{100})^{\textrm t}[/tex]

Or, P = 28,405 × [tex](1+\dfrac{\textrm 2.4}{100})^{\textrm 5}[/tex]

Or, P = 28,405 × [tex](1+0.024)^{\textrm 5}[/tex]

So, The population of city after 5 years = P = 28,405 [tex](1+0.024)^{\textrm 5}[/tex]

Hence, The population of city after 5 years is 28,405 [tex](1+0.024)^{\textrm 5}[/tex]  . Answer

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