Part 1 of 3 Model the pair of situations with exponential functions \( f \) and \( g \). Find the approximate value of \( x \) that makes \( f(x) \) \( =g(x) \). f. initial value of 700 decreasing at a rate of \( 15 \% \) \( g \) : initial value of 20 increasing at a rate of \( 15 \% \) Write the exponential function for \( f \). \( f(x)=\square \) (Use integers or decimals for any numbers in the expression.)

To model the situation for \( f \), since it has an initial value of 700 and is decreasing at a rate of 15%, the function can be expressed as: \( f(x) = 700(1 - 0.15)^x \) This simplifies to: \( f(x) = 700(0.85)^x \) Now, let's look at the function for \( g \). It has an initial value of 20 and is increasing at a rate of 15%. The function can be expressed as: \( g(x) = 20(1 + 0.15)^x \) This simplifies to: \( g(x) = 20(1.15)^x \) To find the approximate value of \( x \) that makes \( f(x) = g(x) \), you will set the two equations equal to each other: \( 700(0.85)^x = 20(1.15)^x \) Now, you can solve for \( x \) using logarithms or numerical methods to find the intersection point of the two functions.