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Sagot :
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:
[tex]P(t) = P(0)(1+r)^t[/tex]
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 [tex]P(0) = 5[/tex]
So
[tex]P(t) = P(0)(1+r)^t[/tex]
[tex]P(t) = 5(1+r)^t[/tex]
In 1981, postage was 18 cents per ounce.
This means that [tex]P(1981 - 1963) = P(18) = 18[/tex]. We use this to find r. So
[tex]P(t) = 5(1+r)^t[/tex]
[tex]18 = 5(1+r)^{18}[/tex]
[tex](1+r)^{18} = \frac{18}{5}[/tex]
[tex]\sqrt[18]{(1+r)^{18}} = \sqrt[18]{3.6}[/tex]
[tex]1 + r = (3.6)^{\frac{1}{18}}[/tex]
[tex]1 + r = 1.0738[/tex]
So
[tex]P(t) = 5(1.0738)^t[/tex]
If the trend had continued through to 2015, what would the postage per ounce be?
2015 - 1963 = 52, so this is P(52).
[tex]P(52) = 5(1.0738)^{52} = 202[/tex]
202 cents, so $2.02.
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