SOLUTION: Write an exponential function for a graph that includes the given points. please help with steps.. please:)) 5. (0, 0.5), (1, 3) 6. (–1, 5), (0.5, 40)

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Write an exponential function for a graph that includes the given points. please help with steps.. please:)) 5. (0, 0.5), (1, 3) 6. (–1, 5), (0.5, 40)      Log On


   

Question 183539: Write an exponential function for a graph that includes the given points.
please help with steps.. please:))
5. (0, 0.5), (1, 3)


6. (–1, 5), (0.5, 40)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first one to get you started

5)

Remember, the general equation for any exponential function is f%28x%29=a%2Ab%5Ex where "a" and "b" are constants

Since we're given the point (0,0.5), this means that x=0 and f%280%29=0.5. So this means that

0.5=a%2Ab%5E0 which simplifies to 0.5=a%2A1 or just 0.5=a. So we now know that a=0.5

Note: I just plugged in the given values into the equation above


Also, since we have another point (1,3), this tells us that when x=1, then f%281%29=3

So plug this in to get: 3=a%2Ab%5E1 which simplifies to 3=a%2Ab

Plug in a=0.5 to get 3=0.5%2Ab and solve for "b" to get b=3%2F0.5 or b=6


So we now know that b=6.


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Answer:

So the exponential equation that goes through the points (0, 0.5) and (1, 3) is y=0.5%2A6%5Ex


Note: you can check by plugging in the original "x" values to get the f(x) values.


Here's a visual confirmation:

Graph of y=0.5%2A6%5Ex through the points (0, 0.5) and (1, 3)