Respuesta :
Answer:
5^x
Step-by-step explanation:
Each level of the question is multiplied by 5 every time x increases by 1.
The exponential function represents the data in the table is f(x) = [tex]5^{x}[/tex] .
What is exponential function?
An exponential function is defined by the formula f(x) = ax, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.
The exponential function is an important mathematical function which is of the form
f(x) = [tex]a^{x}[/tex]
Where a>0 and a is not equal to 1.
x is any real number.
If the variable is negative, the function is undefined for -1 < x < 1.
Here,
“x” is a variable
“a” is a constant, which is the base of the function.
According to the question
Exponential function represents the data in the table
x f(x)
2 25
3 125
4 625
Now,
Putting values in Exponential function equation at :
x f(x)
2 25
f(x) = [tex]a^{x}[/tex]
25 = [tex]a^{2}[/tex]
a = ± 5
Now
x f(x)
3 125
f(x) = [tex]a^{x}[/tex]
125 = [tex]a^{3}[/tex]
a = 5
Therefore ,
a = 5 which will satisfy all the values of x for f(x)
Hence, exponential function represents the data in the table is f(x) = [tex]5^{x}[/tex] .
To know more about exponential function here:
https://brainly.com/question/11487261
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