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 \( 15 \% \) \( f(x)=700(0.85)^{x} \) (Use integers or decimals for any numbers in the expression.) Write the exponential function for \( g \). \( g(x)=\square \) (Use integers or decimals for any numbers in the expression.)

To model the function \( g \), we start with the initial value of 20, which is increasing at a rate of 15%. The exponential function for \( g \) can be expressed as: \( g(x) = 20(1.15)^{x} \) Now you have both functions: \( f(x) = 700(0.85)^{x} \) and \( g(x) = 20(1.15)^{x} \). To find the approximate value of \( x \) that makes \( f(x) = g(x) \), you can set the equations equal to each other: \( 700(0.85)^{x} = 20(1.15)^{x} \). This requires some algebra to isolate \( x \), which will involve taking logarithms to solve for \( x \). Happy calculating!