# The cost of a first-class postage stamp in 1962 was 4. In 1999 it is 33. The cost was (and is) growing exponentially. What was the growth rate?

Jul 25, 2018

The growth rate was 5.87%

#### Explanation:

Time interval is $t = 1999 - 1962 = 37$ years

Initial cost in $1962$ was $a = 4$ unit

Final cost in $1999$ was $y = 33$ unit

Exponential growth function : y=a(1+r)^t ; a>0 , r>0 ,r

is rate of growth in decimal form.

$y = a {\left(1 + r\right)}^{t} \mathmr{and} 33 = 4 {\left(1 + r\right)}^{37}$ or

${\left(1 + r\right)}^{37} = \frac{33}{4} \mathmr{and} {\left(1 + r\right)}^{37} = 8.25$ , taking log on both

sides we get, $37 \log \left(1 + r\right) = \log \left(8.25\right)$ or

$\log \left(1 + r\right) = \log \frac{8.25}{37} \mathmr{and} \log \left(1 + r\right) \approx 0.24769$

$\left(1 + r\right) = {10}^{0.24769} \mathmr{and} 1 + r \approx 1.0587 \therefore r = 0.0587$ or

r%= 0.0587*100 ~~ 5.87 %

The growth rate was 5.87% [Ans]