Question 1202756
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Answer: <font color=red size=4>$5.14</font>


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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)
{{{
drawing(400,400,-3,7,-5,5,
graph(400,400,-3,7,-5,5,-100,1.40*(1.090522)^x),
circle(0,1.40,0.05),circle(0,1.40,0.1),circle(0,1.40,0.15),circle(4,1.98,0.05),circle(4,1.98,0.1),circle(4,1.98,0.15),

locate(0+0.3,1.40,"(0,1.40)"),
locate(4+0.3,1.98,"(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 <font color=red>$5.14</font> in the year 2033.
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