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Use the formula t= ln2 over k that gives the time for a population, with growth rate k, to double, to answer the following questions. The growth model A=6e^0.001t describes the population, A, of a country in millions, t years after 2003. A. What is the country's growth rate? B. (After answering A I will assistance for question B following question A)

User Mzzx
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1 Answer

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Answer:

A. k = 0.001

B. 693 years

Step-by-step explanation:

An exponential function has the following form:


y=a\cdot e^(kt)

Where a is the initial value and k is the growth or decay rate.

So, if the equation is:


A=6e^(0.001t)

Therefore, the growth rate is 0.001.

Now, to know how long will it take the country to double its population, we can use the equation:


t=(\ln 2)/(k)

Where k is the growth rate. So, replacing k by 0.001, we get:


\begin{gathered} t=(\ln 2)/(0.001) \\ t=693.14\approx693\text{ years} \end{gathered}

Therefore, the country will double its population 693 years after 2003

User Joe Holloway
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