Find the formula for the EXPONENTIAL FUNCTION that satsifies the given conditions.
f(0)=8 and f(1)=2.4
f(x)=_____
y = a b^x
8 = a b^0 ... a = 8
2.4 = 8 b^1 ... .3 = b
y = 8 * .3^x
Scott, thanks man!
To find the formula for the exponential function that satisfies the given conditions, we can start by assuming that the exponential function has the form:
f(x) = a * b^x
Here, 'a' represents the initial value of the function (f(0)) and 'b' represents the growth or decay factor.
Given the conditions f(0) = 8 and f(1) = 2.4, we can substitute these values into the equation to get two equations:
(1) f(0) = a * b^0 = a = 8
(2) f(1) = a * b^1 = a * b = 2.4
From equation (1), we know that a = 8. Substituting this into equation (2):
8 * b = 2.4
To find the value of 'b', divide both sides of the equation by 8:
b = 2.4 / 8 = 0.3
Now that we have the value of 'b', we can substitute it back into equation (1) to find the value of 'a':
a = 8
Therefore, the formula for the exponential function that satisfies the given conditions is:
f(x) = 8 * (0.3)^x