Question

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

Answer 1

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:

$\frac{f(x+1)}{f(x)}=\frac{Ab^{x+1}}{Ab^x}=b^{x+1-x}=b$

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

$b=\frac{f(1)}{f(0)}=\frac{1}{5}=0.2$

We can write the exponential model as:

$f(x)=5(0.2)^x$

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