Question

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?

Answer 1

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(1+r)^t or 33 = 4(1+r)^37` or

`(1+r)^37= 33/4 or (1+r)^37= 8.25` , taking log on both

sides we get, `37 log(1+r)= log(8.25)` or

`log(1+r)= log(8.25)/37 or log (1+r) ~~ 0.24769`

`(1+r) =10^ 0.24769 or 1+r~~ 1.0587:. r= 0.0587` or

`r%= 0.0587*100 ~~ 5.87 %`

The growth rate was `5.87%` [Ans]