Question

2. Inflation is at a rate of 7% per year. Evan's favorite bread now costs $1.79. What did it cost 10 years ago? How long
before the cost of the bread doubles?​

Answer 1

Answer:

It cost $0.91 10 years ago.

It takes 10.24 years for the cost of bread to double.

Step-by-step explanation:

The equation for the price of bread after t years has the following format:

$P(t) = P(0)(1+r)^{t}$

In which P(0) is the current price, and r is the inflation rate, as a decimal.

If we want to find the price for example, 10 years ago, we find P(-10).

Inflation is at a rate of 7% per year. Evan's favorite bread now costs $1.79.

This means that $r = 0.07, P(0) = 1.79$. So

$P(t) = P(0)(1+r)^{t}$

$P(t) = 1.79(1+0.07)^{t}$

$P(t) = 1.79(1.07)^{t}$

What did it cost 10 years ago?

$P(-10) = 1.79(1.07)^{-10} = 0.91$

It cost $0.91 10 years ago.

How long before the cost of the bread doubles?

This is t for which P(t) = 2P(0) = 2*1.79. So

$P(t) = 1.79(1.07)^{t}$

$2*1.79 = 1.79(1.07)^{t}$

$(1.07)^{t} = 2$

$\log{(1.07)^{t}} = \log{2}$

$t\log{1.07} = \log{2}$

$t = \frac{\log{2}}{\log{1.07}}$

$t = 10.24$

It takes 10.24 years for the cost of bread to double.