SOLUTION: Write an exponential function for a graph that includes the given points. 1.)(–1, 5),(0.5, 40)

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Question 186668: Write an exponential function for a graph that includes the given points.
1.)(–1, 5),(0.5, 40)
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
y=a%2Ab%5Ex Start with the general exponential equation.


5=a%2Ab%5E%28-1%29 Plug in x=-1 and y=5 Note: this is the point (-1,5)


5=a%2Fb Rewrite the right side with a positive exponent


a=5b Solve for 'a'


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y=a%2Ab%5Ex Go back to the first equation


40=a%2Ab%5E%280.5%29 Plug in x=0.5 and y=40 Note: this is the point (0.5, 40)


40=%285b%29%2Ab%5E%280.5%29 Plug in a=5b


40=5b%5E%281%2B0.5%29 Multiply by adding the exponents.


40=5b%5E%281.5%29 Add


40%2F5=b%5E%281.5%29 Divide both sides by 5.


8=b%5E%283%2F2%29 Reduce and rewrite 1.5 as 3%2F2


8%5E2=b%5E3 Square both sides.


64=b%5E3 Square 8 to get 64


root%283%2C64%29=b Take the cube root of both sides


b=4 Take the cube root of 64 to get 4


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a=5b Go back to the first isolated equation


a=5%284%29 Plug in b=4


a=20 Multiply


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Answer:


So the exponential function that goes through (–1, 5),(0.5, 40) is f%28x%29=20%2A4%5Ex