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A table of data is given Which exponential model best represents the data?

A table of data is given Which exponential model best represents the data?-example-1
A table of data is given Which exponential model best represents the data?-example-1
A table of data is given Which exponential model best represents the data?-example-2
User Melvina
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1 Answer

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28 votes

We have to find the exponential model that best represents the data.

We can write a general model as:


f(x)=A\cdot b^x

Where A is the initial value: the value of f(x) when x = 0.

In this case, from the table, we can see that when x = 0. f(x) = 5, so A has to be 5.

We can also see that the value of f(x) is decreasing with the increase of x. This indicates that the value of b is less than 1.

We can find the value of b as:


(f(x+1))/(f(x))=(Ab^(x+1))/(Ab^x)=b^(x+1-x)=b

Then, if we take x = 0, we can calculate b as:


b=(f(1))/(f(0))=(1)/(5)=0.2

We can write the exponential model as:


f(x)=5(0.2)^x

Answer: f(x) = 5(0.2)^x

User Artem Mirchenko
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