Question

Find the formula for an exponential function that passes through the two points given.
(x,y)=(0,6) and (x,y)=(3,48)
f(x)=

Answer 1

To find the formula for an exponential function that passes through the two points (0, 6) and (3, 48), we can use the general form of an exponential function:

f(x) = a * b^x

where a is the initial value, b is the base or growth factor, and x is the exponent.

Using the two given points, we can write two equations:

When x = 0, f(x) = 6, so:

6 = a * b^0
6 = a

When x = 3, f(x) = 48, so:

48 = a * b^3

We can substitute a = 6 into the second equation:

48 = 6 * b^3
8 = b^3

Taking the cube root of both sides:

b = 2

Now we have the values of a and b, so the formula for the exponential function that passes through the points (0, 6) and (3, 48) is:

f(x) = 6 * 2^x

Therefore, the formula is f(x) = 6*2^x.