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Sagot :
The population at the beginning of 1950 was 2600 thousand people.
Then it started increasing exponentially 23% every decade.
The general form of any exponential function is:
[tex]f(x)=a(b)^x[/tex]Where
a is the initial value
b is the growth/decay factor
x is the number of time periods
y is the final value after x time periods
a. To calculate the growth factor of an exponential function, you have to add the increase rate (expressed as a decimal value) to 1:
[tex]\begin{gathered} b=1+r \\ b=1+\frac{23}{100} \\ b=1.23 \end{gathered}[/tex]b. Considering the initial value a= 2600 thousand people and the growth factor b=1.23, you can express the exponential function in terms of the number of decades, d, as follows:
[tex]f(d)=2600(1.23)^d[/tex]c. Considering that the time unit is measured in decades, i.e d=1 represents 10 years
To determine the corresponding value of the variable d for 1 year, you have to divide 1 by 10
[tex]1\text{year/10years d}=\frac{1}{10}=0.1[/tex]Calculate the growth factor powered by 0.1:
[tex]\begin{gathered} b_{1year}=(1.23)^{0.1} \\ b_{1year}=1.0209\approx1.02 \end{gathered}[/tex]d. Use the factor calculated in item c
[tex]g(t)=2600(1.0209)^t[/tex]
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