Question

I need help number 7

Answer 1

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:

`f(x)=a(b)^x`

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:

`\begin{gathered} b=1+r \\ b=1+(23)/(100) \\ b=1.23 \end{gathered}`

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:

`f(d)=2600(1.23)^d`

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

`1\text{year/10years d}=(1)/(10)=0.1`

Calculate the growth factor powered by 0.1:

`\begin{gathered} b_(1year)=(1.23)^(0.1) \\ b_(1year)=1.0209\approx1.02 \end{gathered}`

d. Use the factor calculated in item c

`g(t)=2600(1.0209)^t`