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)=abx
In 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.
2352.9=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.
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