Question

An investment, initially worth £645.3, grows at a constant continuous rate of 0.05. After how many years will it be

Answer 1

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:

$y = a(1 + r)^t$

Where:

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

The number of years

So, we have:

$y = 645.3(1.05)^t$

When the investment becomes 29437.2, the equation becomes

$29437.2 = 645.3(1.05)^t$

Divide both sides by 645.3

$45.6=1.05^t$

Take the logarithm of both sides

$\log(45.6)=\log(1.05)^t$

This gives

$\log(45.6)=t\log(1.05)$

Make t the subject

$t = \frac{\log(45.6)}{\log(1.05)}$

$t = 78.3$

Hence, it will take 78.3 years for the investment to reach £29437.2

Read more about exponential functions at:

brainly.com/question/11464095