SOLUTION: I really need your help in writing an exponential function whose graph passes through the points (0,-5) and (-2,-20). Then determining whether the function represents exponential g

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Question 189524This question is from textbook Algebra 2
: I really need your help in writing an exponential function whose graph passes through the points (0,-5) and (-2,-20). Then determining whether the function represents exponential growth or decay. I would really appreciate any help! This question is from textbook Algebra 2

Found 2 solutions by scott8148, Edwin McCravy:
Answer by scott8148(6628)   (Show Source): You can put this solution on YOUR website!
a general form would be ___ y = m * n^x

for the first point ___ -5 = m * n^0 ___ -5 = m * 1 ___ -5 = m

for the second point ___ -20 = -5 * n^-2 ___ 4 = n^-2 ___ 1/4 = n^2 ___ 1/2 = n

so the function is ___ y = -5 * (1/2)^x

since the base for the exponent is fractional (<1), the function represents exponential decay

Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
Edwin's solution:
I claim it is a growth not a decay!

It has to be growth because when x goes from a smaller value -2
to larger value 0, y also grows from a smaller value -20 to a 
larger value -5.  That is a growth.

We start with the basic exponential equation:



Then we substitute the point (0,-5)









So the exponential equation  is now



Now we substitute the other point (-2, -20)



And simplify:


 
Multiply both sides by 



Divide both sides by -20









So the equation  is now



The graph looks like this:



which shows it's a growth.

Edwin

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