Final answer:
The growth rate of the cost of a first-class postage stamp can be found using the exponential growth formula. The growth rate is approximately 0.066. Using the same formula, the cost of a first-class postage stamp in 2010 would be approximately $2.04.
Step-by-step explanation:
To find the growth rate, we can use the exponential growth formula:
A = P(1 + r)^t
Where A is the final amount, P is the initial amount, r is the growth rate, and t is the time in years. We know that in 1962 the cost of a postage stamp was $4 and in 1999 it was $33, so we can plug these values into the formula to find the growth rate:
33=4(1 + r)^37
Divide both sides of the equation by 4:
(1 + r)^37 = 33/4
Take the 37th root of both sides:
1 + r = (33/4)^(1/37)
Subtract 1 from both sides:
r = (33/4)^(1/37) - 1
Using a calculator, we find that r is approximately 0.066.
To find the cost of a stamp in 2010, we can use the same formula:
C = P(1 + r)^t
Where C is the cost in 2010, P is the initial cost, r is the growth rate, and t is the time in years. We know that P is $4, r is 0.066, and t is 2010 - 1962 = 48. Plugging in these values, we can calculate:
C = 4(1 + 0.066)^48
Using a calculator, we find that the cost of a first-class postage stamp in 2010 would be approximately $2.04.