b Find the function's initial value and multiplier.
C
c What percentage change does a multiplier of 0.85 correspond to?
A
aDiagram:
B
b f(x)=10(2.3)^x
C
c See solution.
Practice makes perfect
a To graph the function, we have to calculate a few ordered pairs through which the function's graph passes. To do so, we choose a few x-values and calculate their corresponding y-values.
x
2(0.75)^x
y
- 2
2(0.75)^(- 2)
3.56
- 1
2(0.75)^(- 1)
2.67
0
2(0.75)^0
2
1
2(0.75)^1
1.5
2
2(0.75)^2
1.125
3
2(0.75)^3
0.84
We now plot the points and connect them with a smooth curve.
b The general form of an exponential function has a specific format.
f(x)=ab^xIn this equation, a is the initial value and b is the multiplier. If we divide 52.9 by its preceding value, we can calculate the multiplier.
52.9/23=2.3
The multiplier is 2.3. When we know the multiplier, we can substitute one of the ordered pairs into the function rule and solve for a. Let's use the pair (1,23).
c From the equation, we see that the initial value is 75 and the multiplier is 0.85.
f(x)= 75( 0.85)^x
A multiplier of 0.85 corresponds to a decrease of 15 %. A possible context based on this equation could be that you have $75 deposited in your bank account and spend 15 % of what is left in your bank account each month.
