Question 1202756: In 2018, a 2-liter of Coca-Cola cost $1.40. In 2022, the cost is $1.98.
Write an exponential equation to describe the rate of inflation over this time period. Let t = 0 correspond to 2018, and let C be the cost of a 2-liter. Round any numbers calculated to at least four decimal places.
C = ?
If inflation continues at the same rate, how much will a 2-liter of Coke cost in 2033?
Found 2 solutions by math_tutor2020, greenestamps:
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Answer: $5.14
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Explanation:
I'll use x in place of t, and y in place of C.
x = t
y = C
One template of an exponential function is
y = a*b^x
x = 0 corresponds to the year 2018.
When x = 0, the cost is y = 1.40
The point (0,1.40) is on the exponential curve.
It is the y intercept.
The gap from 2022 to 2018 is 4 years (since 2022-2018 = 4).
x = 4 corresponds to the year 2022.
We have x = 4 pair with y = 1.98
The point (4,1.98) is also on the exponential curve.
Plug in the coordinates of the 1st point.
y = a*b^x
1.40 = a*b^0
1.40 = a*1
1.40 = a
a = 1.40
This is the initial value.
We have
y = a*b^x
update to
y = 1.40*b^x
Plug in the coordinates of the 2nd point
y = 1.40*b^x
1.98 = 1.40*b^4
1.98/1.40 = b^4
1.414286 = b^4
b = (1.414286)^(1/4)
b = 1.090522
The result is approximate
Therefore,
y = 1.40*b^x
updates to
y = 1.40*(1.090522)^x
Graph of y = 1.40*(1.090522)^x through the points (0,1.40) and (4,1.98)
GeoGebra and Desmos are two graphing options I recommend.
The year 2033 is 2033-2018 = 15 years after 2018.
Plug in x = 15
y = 1.40*(1.090522)^x
y = 1.40*(1.090522)^(15)
y = 5.13623051169986
y = 5.14
The two-liter coke is estimated to cost around $5.14 in the year 2033.
Answer by greenestamps(13214)  (Show Source):
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