Model the data using an exponential function f(x)=Ab^x begin{array}{|l|l|l|}hline x&0&1&2hline f(x)&125&25&5hlineend{array}

Braxton Pugh

Braxton Pugh

Answered question

2021-03-07

Model the data using an exponential function f(x)=Abx
x012f(x)125255

Answer & Explanation

Viktor Wiley

Viktor Wiley

Skilled2021-03-08Added 84 answers

Given- Consider the data,
x012f(x)125255
To model- The above data using an exponential function f(x)=Abx
Explanation- As per the question, we have to model the above data using the given exponential expression as,
f(x)=Abx (1)
Now, using first value x=0 and f(x)=125, we get from the above expression,
f(0)=Ab0
125=A1
125=A
So, equation (1) becomes,
f(x)=125bx
Now, using second value x=1 and f(x)=25, we get from the above expression,
f(1)=125b1 (2)
25=125b
The above expression can be written as,
b=25125
b=15
So, equation (2), becomes,
f(x)=125(15)x (3)
Now, to check the above expression, we can use the third value as x=2 and f(x)=5, we get,
5=125(15)2
5=125125
5=5
So, the expression f(x)=125(15)x is correct expression.
Answer- Hence, the exponential expression which models the given data is
f(x)=125(15)x

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