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

Algebra ->  Exponential-and-logarithmic-functions -> 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      Log On


   

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) About Me  (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) About Me  (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:

y+=+A%2AB%5Ex

Then we substitute the point (0,-5)

y+=+A%2AB%5Ex

-5+=+A%2AB%5E0

-5+=+A%2A1

-5+=+A+

So the exponential equation y+=+A%2AB%5Ex is now

y+=+-5%2AB%5Ex

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

-20+=+-5%2AB%5E%28-2%29

And simplify:

-20+=+-5%2A%281%2FB%5E2%29
 
Multiply both sides by B%5E2

-20B%5E2+=+-5

Divide both sides by -20

B%5E2+=+%28-5%29%2F%28-20%29

B%5E2+=+1%2F4

B+=+sqrt%281%2F4%29

B+=+1%2F2

So the equation y+=+-5%2AB%5Ex is now

y+=+-5%2A%281%2F2%29%5Ex

The graph looks like this:

graph%28200%2C100%2C-3%2C3%2C-40%2C10%2C-5%2A%28.5%29%5Ex%29

which shows it's a growth.

Edwin