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Given:
Initial cost of living = $44,000
Rate of increase = 5% = 0.05
To find:
The cost of living in 20 years.
Solution:
The exponential growth model is:
[tex]y=a(1+r)^t[/tex]
Where, a is the initial value, r is the growth rate and t is the number of years.
Putting [tex]a=44000,r=0.05, t=20[/tex] in the above model, we get
[tex]y=44000(1+0.05)^{20}[/tex]
[tex]y=44000(1.05)^{20}[/tex]
[tex]y=116745.099026 [/tex]
[tex]y\approx 116745.10 [/tex]
Therefore, the cost of living in 20 years is about $116745.10.