Question

The cost of a can of Coca Cola in 1960 was $ 0.10 . The exponential function that models the cost of a Coca Cola by year is given below, where t is the number of years since 1960 . C ( t ) = 0.10 e^0.0576t Find the expected cost of a can of Coca Cola in 1990 , 2000 , 2015 and 2040 (rounded to the nearest cent). They expected the cost of Coca Cola to be $-------- in 1990 , $ --------in 2000 , $-------- in 2015 , and $ -------in 2040 .

Answer 1

The exponential function that models the cost of a can of Coca Cola is given by C(t) = 0.10e^0.0576t where $ 0.10 is the cost of a can of Coca Cola in 1960 and t is the number of years since 1960 .

1. In 1990, t = 30, so that C(30) = 0.10e^0.0576*30 = 0.10e^1.728 = 0.10* 5.629383874 = 0.56 ( on rounding off to the nearest cent). Thus, the expected cost of a can of Coca Cola in 1990 is $ 0.56.

2. In 2000, t = 40, so that C(30) = 0.10e^0.0576*40 = 0.10e^2.304= 0.10* 10.01415908= 1.00( on rounding off to 2 decimal places). Thus, the expected cost of a can of Coca Cola in 1990 is $1.00.

3. . In 2015, t = 55, so that C(30) = 0.10e^0.0576*55 = 0.10e^3.168 = 0.10* 23.75991697= 2.38 ( on rounding off to the nearest cent). Thus, the expected cost of a can of Coca Cola in 1990 is $2.38.

4. In 2040, t = 80, so that C(30) = 0.10e^0.0576*80 = 0.10e^4.608 = 0.10* 100.2833822= 10.03( on rounding off to the nearest cent). Thus, the expected cost of a can of Coca Cola in 1990 is $10.03.