An exponential function can generally be represented in the form \( f(x) = a \cdot b^x \), where \( a \) is the initial value (the value of the function when \( x = 0 \)) and \( b \) is the base of the exponential function.
Given that we are looking for an exponential function with an initial value of 500, we need a function where \( a = 500 \).
Among the provided options, the equation that fits this criterion is:
\[ f(x) = 500(2)^x \]
This function has an initial value of 500, as when \( x = 0 \):
\[ f(0) = 500 \cdot 2^0 = 500 \cdot 1 = 500 \]
So, the correct choice is:
\[ f(x) = 500(2)^x \]
Which equation represents an exponential function with an initial value of 500?
f(x) = 100(5)x
f(x) = 100(x)5
f(x) = 500(2)x
f(x) = 500(x)2
1 answer
1 answer