The values of two functions, f and g, are given in a table. One, both, or neithe

mattgondek4

mattgondek4

Answered question

2021-09-20

The values of two functions, f and g, are given in a table. One, both, or neither of them may be exponential. Decide which, if any, are exponential, and give the exponential models for those that are.
x21012f(x)0.30.92.78.124.3g(x)31.50.750.3750.1875

Answer & Explanation

Maciej Morrow

Maciej Morrow

Skilled2021-09-21Added 98 answers

Step 1
Recall:
For the exponential function f(x)=Abx
1. f(0)=A
2. If x increases by 1, f(x) is multiplied by b
Step 2
Observe the table for f(x)
x21012f(x)0.30.92.78.124.3
Step 3 NKS Calculate the ratios f(x)f(x1)
to see by how much f(x) increases when x increases by 1
x21012f(x)0.30.92.78.124.3f(x)f(x1)3333
Step 4
Note that there exists a constant b=3
such that condition 2 is satisfied, which means that f is exponential,
f(x)=A3x
Furthermore, A=f(0)=2.7, so
f(x)=2.73x
Step 5
Observe that table for g(x):
x21012g(x)31.50.750.3750.1875
Step 6
Calculate the ratios g(x)g(x1), to see by how much g(x) incresded when x increases by 1
x21012g(x)31.50.750.3750.1875g(x)g(x1)0.50.50.50.5
Step 7
Note that there exists a constant b=0.5
such that condition 2 is satisfied, which means that g is exponential,
g(x)=A(0.5)x
Furthermore, A=g(0)=0.75, so NSk g(x)=0.75(0.5)x
Since 0.5x=(21)x=2x, we can write
g(x)=0.752x

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