Question

If the cost of a loaf of bread is now $2.75 and is increasing at 5% per year, what will it cost 10 years from now. Write an exponential equation for this scenario then use it to solve the problem

Answer 1

To estimate the cost (C) after t years with an increasing rate r, use the formula below:

$C(t)=C_0*\left(1+r\right)^t$

In this question:

C0 = initial cost = $2.75

r = rate = 0.05

t = time = 10 years

Substituting the values in the equation:

$\begin{gathered} C(10)=2.75*\left(1+0.05\right)^{10} \\ C(10)=2.75*1.05^{10} \\ C(10)=2.75*1.629 \\ C(10)=4.48 \end{gathered}$

Answer:

Equation:

$\begin{gathered} C(t)=2.75(1+0.05)^t \\ C(10)=2.75(1+0.05)^{10} \end{gathered}$

Cost: C(10) = $4.48.