Given the points (1,2) and (5, 50):a. Find a linear function of the form y = ax +b that goes through the two points.y 12x-10Editb. Find an exponential function of the form y = a - b* that goes through the two points.Round your answers to three decimal places.y a b*where a =and bc. Find a power function of the form y = ax2 that goes through the two points.y Edit

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Asked Oct 29, 2019
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Given the points (1,2) and (5, 50):
a. Find a linear function of the form y = ax +b that goes through the two points.
y 12x-10
Edit
b. Find an exponential function of the form y = a - b* that goes through the two points.
Round your answers to three decimal places.
y a b*where a =
and b
c. Find a power function of the form y = ax2 that goes through the two points.
y Edit
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Given the points (1,2) and (5, 50): a. Find a linear function of the form y = ax +b that goes through the two points. y 12x-10 Edit b. Find an exponential function of the form y = a - b* that goes through the two points. Round your answers to three decimal places. y a b*where a = and b c. Find a power function of the form y = ax2 that goes through the two points. y Edit

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Expert Answer

Step 1
(a)
Consider the given two points on the line as (1,2) and (5,50).
Note that, the equation of line passing through two points (x,,y) and (x,,y) is given
by
Hence, the calculate the equation of line from two points (1, 3) and (3, -3) as follows
( (x, 1;) = (1,2)
(x,.y2)(5,50)
y-2
50 2
x-1
5 1
-1
y-2
48
4
48
y-2
4
(x-1)
y 12x-10
help_outline

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(a) Consider the given two points on the line as (1,2) and (5,50). Note that, the equation of line passing through two points (x,,y) and (x,,y) is given by Hence, the calculate the equation of line from two points (1, 3) and (3, -3) as follows ( (x, 1;) = (1,2) (x,.y2)(5,50) y-2 50 2 x-1 5 1 -1 y-2 48 4 48 y-2 4 (x-1) y 12x-10

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Step 2
(b)
Consider the exponential function as y = ab*.
Since the function passing through two points (1,2) and (5,50), the constant value can be
obtained as follows
((x,y)(1.2) 1)
50 ab ((x, y)= (5,50)...(2)
2 ab
50 2b4
b 25
b 1.057
2
Substitute b 1.057 in the equation 2 ab and solve for a
a(1.057) 2
2
1.892
=
1057
y =(1.892)(1.057)
Thus
the
exponential
function
is
where
a 1.892 and b=1.057
help_outline

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(b) Consider the exponential function as y = ab*. Since the function passing through two points (1,2) and (5,50), the constant value can be obtained as follows ((x,y)(1.2) 1) 50 ab ((x, y)= (5,50)...(2) 2 ab 50 2b4 b 25 b 1.057 2 Substitute b 1.057 in the equation 2 ab and solve for a a(1.057) 2 2 1.892 = 1057 y =(1.892)(1.057) Thus the exponential function is where a 1.892 and b=1.057

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