Question

Sue owes an amount of £800
Each month, she pays back 20% of the amount she still owes.
How much will she still have left to pay at the end of five months?

Answer 1

Answer:

She will have £262 left to pay at the end of five months.

Step-by-step explanation:

Exponential equation for an amount:

A exponential equation for an amount that decays has the following format:

$A(t) = A(0)(1-r)^{t}$

In which A(0) is the initial amount, r is the decay rate, as a decimal, and t is the time measure.

Sue owes an amount of £800

This means that $A(0) = 800$

Each month, she pays back 20% of the amount she still owes.

This means that $r = 0.2$

So

$A(t) = A(0)(1-r)^{t}$

$A(t) = 800(1-0.2)^{t}$

$A(t) = 800(0.8)^{t}$

How much will she still have left to pay at the end of five months?

This is A(5). So

$A(5) = 800(0.8)^{5} = 262$

She will have £262 left to pay at the end of five months.