Question

the cost of a can of coca-cola in 1960 was $ 0.10 . the function that models the cost of a coca-cola by year is c ( t )

Answer 1

The cost of the Coca-Cola can will be $1 in the year 2000.

Given that the cost of a can of Coca-Cola can in 1960 = $0.10

The function which models the cost of a Coca-Cola by year 't' is

c(t) =   $0.10e^{0.0576t}$.

Here, 't' denotes the number of years since 1960.

c(t) is an exponential function.

We have to find the year in which the cost of a can will be $1.

So substitute c(t) = 1, we get,

  1 =   $0.10e^{0.0576t}$

⇒ $10 = e^{0.0576t}$

We have, $ln(e^x) = x$ .

Taking logarithm on both sides, we get,

log(10) = 0.0576t

⇒  $t=\frac{ln(10)}{0.0576}$  = 39.97 ≈ 40 years .

Thus the cost of a can of Coca-Cola will be $1 in the year, 1960 + 40 = 2000.

The question was incomplete. Find the complete question at:

The cost of a can of Coca-Cola in 1960 , was $0.10. The function that models the cost of a Coca-Cola by year is C(t)=0.10e^(0.0576t) , where t is the number of years since 1960 . In what year is it expected that a can of Coca-Cola will cost $1.00 ?

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