6. Jai works at an electronics store. The function to describe Jai's total weekly earnings, \( t(s) \), as a function of her sales, \( s \) can be represented by \( t(s)=0.05 s+600 \). reperese a) How much did Jai earn if her sales for the week were \( \$ 950 \). b) Find the inverse function. Use that function to determine what her sales were for one week if she earned \( \$ 775 \).

To solve the problem, we will address each part step by step. ### Part a: Calculate Jai's earnings for sales of $950 The function for Jai's total weekly earnings is given by: \[ t(s) = 0.05s + 600 \] To find Jai's earnings when her sales \( s \) are $950, we substitute \( s = 950 \) into the function: \[ t(950) = 0.05(950) + 600 \] Calculating \( 0.05 \times 950 \): \[ 0.05 \times 950 = 47.5 \] Now, add this to 600: \[ t(950) = 47.5 + 600 = 647.5 \] Thus, Jai earned **$647.50** when her sales for the week were $950. ### Part b: Find the inverse function and determine sales for earnings of $775 To find the inverse function, we start with the original function: \[ t(s) = 0.05s + 600 \] We will replace \( t(s) \) with \( y \): \[ y = 0.05s + 600 \] Next, we solve for \( s \) in terms of \( y \): 1. Subtract 600 from both sides: \[ y - 600 = 0.05s \] 2. Divide both sides by 0.05: \[ s = \frac{y - 600}{0.05} \] Now, we can express the inverse function \( t^{-1}(y) \): \[ t^{-1}(y) = \frac{y - 600}{0.05} \] Now, we will use this inverse function to determine Jai's sales when she earned $775. We substitute \( y = 775 \): \[ s = t^{-1}(775) = \frac{775 - 600}{0.05} \] Calculating \( 775 - 600 \): \[ 775 - 600 = 175 \] Now, divide by 0.05: \[ s = \frac{175}{0.05} = 3500 \] Thus, Jai's sales for the week when she earned **$775** were **$3500**.