If f(x) is an exponential function where f(2.5)=26 and f(6.5)=81, then find the value of f(12), to the nearest hundredth.

Given:

f(x) is an exponential function.

To find:

The value of f(12), to the nearest hundredth.

Solution:

The general exponential function is

For, x=2.5,

         ...(i)

For, x=6.5,

         ...(ii)

Divide (ii) by (i).

Taking 4th root on both sides, we get

Putting b=1.32855 in (i), we get

Now, the required function is

Putting x=12, we get

Therefore, the value of f(12) is 386.422.

Hence, the surface area of cone is:

282.6 cm^2 which is approx 283 cm^2.

Step-by-step explanation:

We are given:

           i.e. r=5 cm.

               i.e. h=12 cm.

                    i.e. l=13 cm.

Now we know that the surface area(S.A.) of cone is given by:

Hence by putting the value of l,r and π in the formula we get:

Hence the surface area of cone is 282.6 cm^2 which is approx 283 cm^2.