In 1991, the cost of mailing a 1 oz. first-class letter was 29 cents, and the inflation rate was 4.6%. If the inflation rate stayed constant, the function C(t) = .29(1.046)t would represent the cost of mailing a first-class letter as a function of years since 1991.
2. In 2007, the cost of mailing a first-class letter was 41 cents. Has the inflation rate stayed constant since 1991? Explain.

Question

In 1991, the cost of mailing a 1 oz. first-class letter was 29 cents, and the inflation rate was 4.6%. If the inflation rate stayed constant, the function C(t) = .29(1.046)t would represent the cost of mailing a first-class letter as a function of years since 1991.
2. In 2007, the cost of mailing a first-class letter was 41 cents. Has the inflation rate stayed constant since 1991? Explain.

elenathehomeschooler · Answer

@jim_thompson5910  can you help?

jim_thompson5910 · Answer

2007 - 1991 = 16

so plug t = 16 into the C(t) function and tell me what you get

elenathehomeschooler · Answer

i got -15.40

jim_thompson5910 · Answer

you should get some number between 0 and 1

elenathehomeschooler · Answer

0.03

jim_thompson5910 · Answer

$$\Large C(t) = 0.29(1.046)^t$$

$$\Large C(16) = 0.29(1.046)^{16}$$

$$\Large C(16) = \underline{ \ \ \ \ \ \ \ \ \ }$$

fill in the blank

jim_thompson5910 · Answer

use a calculator to evaluate `0.29*(1.046)^16`

elenathehomeschooler · Answer

it will be 0.596

jim_thompson5910 · Answer

so approx 60 cents

if we use the C(t) function, the price should be 60 cents
but it's actually 41 cents

so the rate of inflation is NOT the same (it's NOT constant). The rate of inflation has gone down