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An investment, initially worth £645.3, grows at a constant continuous rate of 0.05. After how many years will it be
worth £29437.2? (find t)
Give your answer to 1 decimal place

Sagot :

MrRoyal

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:

  • Initial worth: 645.3
  • Rate: 0.05

Exponential functions

An exponential function is represented as:

[tex]y = a(1 + r)^t[/tex]

Where:

  • a represents the initial value
  • r represents the rate.

The number of years

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

Read more about exponential functions at:

https://brainly.com/question/11464095

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