SME
Grade 9 Math · Algebra 1
Exponential functions: growth and decay
Use this for “y = 300(2)ˣ. What is y when x = 3?” and other growth and decay models.
Chart
y-intercept (0, 300)
Horizontal asymptote y = 0
f(3) = 2,400
This is an example. Type your own values to start a new problem.
y
=
a
(
)
x
x
Input
example
y
Output
calculated
Formulas
y
=
a
×
b
x
2,400
=
300
×
2
3
Assumptions
•
a is the value at x = 0, the y-intercept.
•
b > 1 grows and 0 < b < 1 decays (b = 1 is a flat line).
•
Each step of 1 in x multiplies y by b.
Step-by-step
WE KNOW
x = 3, a = 300, b = 2
FIND
output (y)
Step 1 · Find output (y)
Use y = a × bˣ
Raise
b
to
the
power
x
,
then
multiply
by
a
:
each
step
of
1
in
x
multiplies
by
b
once
more.
y
=
300
×
2
3
y
=
300
×
8
y
=
2,400
Check
Put the numbers back in. Both sides should match.
2,400
=
300
×
2
3
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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