Question

Questions 24-25. In 1963, postage was 5 cents per ounce. In 1981, postage was 18 cents per ounce.
If the trend had continued through to 2015, what would the postage per ounce be?
(round to the nearest central

The answer posted "42.55" is incorrect.

Answer 1

Answer:

The postage per ounce would be of $2.02.

Step-by-step explanation:

Exponential model:

The postage, in t years after 1963, follows the following format:

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

In which P(0) is the initial value and r is the growth rate, as a decimal.

In 1963, postage was 5 cents per ounce.

This means that $P(0) = 5$

So

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

$P(t) = 5(1+r)^t$

In 1981, postage was 18 cents per ounce.

This means that $P(1981 - 1963) = P(18) = 18$. We use this to find r. So

$P(t) = 5(1+r)^t$

$18 = 5(1+r)^{18}$

$(1+r)^{18} = \frac{18}{5}$

$\sqrt[18]{(1+r)^{18}} = \sqrt[18]{3.6}$

$1 + r = (3.6)^{\frac{1}{18}}$

$1 + r = 1.0738$

So

$P(t) = 5(1.0738)^t$

If the trend had continued through to 2015, what would the postage per ounce be?

2015 - 1963 = 52, so this is P(52).

$P(52) = 5(1.0738)^{52} = 202$

202 cents, so $2.02.