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The investment growth is an illustration of an exponential function.
It will take 78.3 years for the investment to reach £29437.2
The given parameters are:
An exponential function is represented as:
[tex]y = a(1 + r)^t[/tex]
Where:
So, we have:
[tex]y = 645.3(1.05)^t[/tex]
When the investment becomes 29437.2, the equation becomes
[tex]29437.2 = 645.3(1.05)^t[/tex]
Divide both sides by 645.3
[tex]45.6=1.05^t[/tex]
Take the logarithm of both sides
[tex]\log(45.6)=\log(1.05)^t[/tex]
This gives
[tex]\log(45.6)=t\log(1.05)[/tex]
Make t the subject
[tex]t = \frac{\log(45.6)}{\log(1.05)}[/tex]
[tex]t = 78.3[/tex]
Hence, it will take 78.3 years for the investment to reach £29437.2
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