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)=
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.