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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)

Respuesta :

Answer:

A. k = 0.001

B. 693 years

Explanation:

An exponential function has the following form:

[tex]y=a\cdot e^{kt}[/tex]

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

So, if the equation is:

[tex]A=6e^{0.001t}[/tex]

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:

[tex]t=\frac{\ln 2}{k}[/tex]

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

[tex]\begin{gathered} t=\frac{\ln 2}{0.001} \\ t=693.14\approx693\text{ years} \end{gathered}[/tex]

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

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