Question

I need help with an exponential graph please

Answer 1

If the function is exponential, then, it is of the form:

`f(x)=ab^x`

It is necessary to find the values of a and b, by using the values of the given table.

To calculate b, find the constant which result of the quotient between consecutive values of f(x). You have:

450/250 = 1.8

810/450 = 1.8

Then, b = 1.8

The function is:

`f(x)=a(1.8)^x`

next, it is necessary to find the value of a, a is the value of f(x) when x=0. To know what is such value, consider that values of x previous to x=12 are the result of the multiplication of a number by 1.8.

Then, for x=11, it is necessary:

f(11) =250/1.8 = 138.88

f(10) = 138.88/1.8 = 77.16 = 250/(1.8²)

and so on ...

for x=0

f(0) = 250/(1.8¹²) = 0.216

Then, a = 0.21

Finally, the function is:

`f(x)=0.21(1.8)^x`

Then, for the other values of x in the table you obtain:

`\begin{gathered} f(15)=0.21(1.8)^(15)=1,416.8 \\ f(16)=0.21(1.8)^(16)=2,550.23 \\ f(17)=0.21(1.8)^(17)=4,590.41 \end{gathered}`