Respuesta :
Given:
Population is 2005 = 35,700
growth rate = 4% = 0.04
To find:
The population in 2030.
Solution:
The general exponential growth model is
[tex]y=a(1+r)^t[/tex]
where, a is initial value, r is growth rate and t is time in years.
Let the initial year is 2005. So, number of years between 2005 to 2030 is
[tex]2030-2005=25[/tex]
Putting a=35,700, r=0.04 and t=25 in the above model.
[tex]y=35,700(1+0.04)^{25}[/tex]
[tex]y=35,700(1.04)^{25}[/tex]
[tex]y=35,700(2.665836)[/tex]
[tex]y=95170.3452[/tex]
Approximate the value to the nearest whole number.
[tex]y\approx 95,170[/tex]
Therefore, population of the district will be about 95,170.
Amount in 2030 is $95,169
Given that:
Amount invested = $35,700
Growth rate = 4% = 0.04
Time invested = 2030 - 2005
Time invested = 25 year
Find:
Amount in 2030
Computation:
A = P[1+r]ⁿ
Amount in 2030 = 35700[1+0.04]²⁵
Amount in 2030 = 35700[1.04]²⁵
Amount in 2030 = 35700[2.6658]
Amount in 2030 = $95,169
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