Download Finding an Exponential Equation with Two Points and an Asymptote

Finding an Exponential Equation with
Two Points and an Asymptote
Finding an Exponential Equation with
Two Points and an Asymptote
Find an exponential function whose asymptote is y=0
and passes through the points (2,16) and (6,256).
Substitute into either
Substitute into
equation to find a
Larger
x
y=ab twice
2
exponent
6
first
256  ab
÷ 16  ab
Divide #s
16  b
4
16  b
2b
4
2
Subtract
Exponents
Find the
Root
16  a  2 
16  a  4
4a
y  4  2
x
Finding an Exponential Equation with
Two Points and an Asymptote
Find an exponential function that passes through (-3,239)
and (2,-3) and has a horizontal asymptote of y = -4.
Substitute into twice:
3  ab  4
2
+4
3
+4
239  ab  4
+4
Divide #s
÷
y  ab  c
Larger
exponent
first
+4
1  ab 2
243  ab
5
1
243  b
5 1 b
243
1
3 b
Rewrite into
y=abx
3
Subtract
Exponents
Find the
Root
x
Asymptote
c=-4
Substitute into either
equation to find a
1 2
3
1
9
1
9
3  a    4
3  a  4
1 a
9a
y  9

1 x
3
4
Finding an Exponential Equation with
Two Points and an Asymptote
Find an exponential function that passes through (3,12.5)
and (4,11.25) and has a horizontal asymptote of y = 10.
Substitute into twice:
11.25  ab  10
4
– 10
– 10
12.5  ab  10
– 10
Divide #s
÷
3
– 10
1.25  ab 4
2.5  ab3
0.5  b
y  ab  c
x
Larger
exponent
first
Rewrite into
y=abx
Subtract
Exponents
Asymptote
c=10
Substitute into either
equation to find a
3
12.5  a  0.5   10
12.5  0.125a 10
2.5  0.125a
20  a
y  20  0.5   10
x
Warning: This is not addressed a lot in the homework but will be assessed.