Answer:
Step-by-step explanation:
Matching the form
A = A0·e^(kt)
to the given equation
A = 8·e^(.005t)
we can identify the value of k as being 0.005.
k = 0.005
___
The doubling time is given by the formula ...
t = ln(2)/k = ln(2)/0.005 ≈ 138.63
It will take about 139 years for the population to double.
a)
We have that the countries growth rate k is given below as
[tex]k=0.5 \%[/tex],
b)
And it will take the country [tex]t=139years[/tex] to double its population.
a)
From the question we are told that:
Formula time for a population growth rate double
[tex]t=\frac{In2}{k}[/tex]
Growth modes
[tex]A=8e^{0.005t}[/tex]
With [tex]e^{0.005t}[/tex]as the Growth factor
Therefore
[tex]e^{0.005t}=2[/tex]
Natural Logarithm
[tex]Ine^{0.005(\frac{In2}{k})}=In2[/tex]
[tex]0.005(\frac{In2}{k})}=In 2[/tex]
[tex]k=0.005[/tex]
b)
Generally, the equation for time t is mathematically given by
[tex]t=\frac{In2}{k}[/tex]
Therefore
[tex]t=\frac{In2}{0.005}[/tex]
[tex]t=138.61[/tex]
[tex]t=139years[/tex]
In conclusion
Is the countries growth rate k is given below as
[tex]k=0.005[/tex]
[tex]k=0.5 \%[/tex]
And with the growth rate we derived How long will it take the country to double its population as
[tex]t=139years[/tex]
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