An exponential function of the form y=a(b)^{x} passes through the

hunterofdeath63

hunterofdeath63

Answered question

2021-12-12

An exponential function of the form y=a(b)x passes through the points
(2,1176) and (5, 50421). Determine the values of a and b algebraically.

Answer & Explanation

Kindlein6h

Kindlein6h

Beginner2021-12-13Added 27 answers

Graph
An exponential function of the form y=a(b)x passes through the points (2,1176) and (5, 50421). Determine the values of a and b algebraically.
Solution
y=abx
passes through (2,1176) and (5,50421)
1176=ab2 (1)
50421=ab5 (2)
Now from (1) we get,
a=1176b2
(2) we get,
50421=1176b2b5
504211176=b3
3438=b3
72=b
(1) we get,
1176=a.494
a=96
Therefore the value of a=96 and b=72.
limacarp4

limacarp4

Beginner2021-12-14Added 39 answers

Step 1
Exponential function is y=abx given points are (2,1176) (5,50421) find the values of a and b algebraically
Step 2
By using the given points lets form an equations
(2,1176)1176=ab2 (1)
(5,50421)50421=ab5 (2)
lets divide (2) by (1)
504211176=ab5ab2
42.875=b3
b=3{42.875}
b=3.5
substitute b value in eq (1) we have
1176=a(3.5)2
1176=a(12.25)
a=96
Thus y=96(3.5)x

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