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)

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) (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 where "a" and "b" are constants

Since we're given the point (0,0.5), this means that and . So this means that

which simplifies to or just . So we now know that

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 , then

So plug this in to get: which simplifies to

Plug in to get and solve for "b" to get or

So we now know that .

======================================

Answer:

So the exponential equation that goes through the points (0, 0.5) and (1, 3) is

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

Here's a visual confirmation:

Graph of through the points (0, 0.5) and (1, 3)

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