a) You have a \( \$ 60 \) gift card to a local café and spend \( \$ 3.50 \) of that to buy a pastry every day. \( f(x)= \) b) A sample of 500 bacteria is treated with a medicine that kills half of them every hour. \( f(x)= \) c) A gym has a one-time sign-up fee of \( \$ 90 \) and monthly memberhip dues of \( \$ 20 \). \( f(x)= \) d) A job offers a starting salary of \( \$ 38,000 \) with yearly raises of \( 4 \% \). \( f(x)= \)

Let's define the functions for each scenario step by step. ### a) Gift Card Spending You start with a \( \$ 60 \) gift card and spend \( \$ 3.50 \) each day. Let \( x \) represent the number of days. The function \( f(x) \) representing the remaining balance on the gift card after \( x \) days can be expressed as: \[ f(x) = 60 - 3.5x \] ### b) Bacteria Treatment You start with a sample of 500 bacteria, and half of them are killed every hour. Let \( x \) represent the number of hours. The function \( f(x) \) representing the number of bacteria remaining after \( x \) hours can be expressed as: \[ f(x) = 500 \cdot \left(\frac{1}{2}\right)^x \] ### c) Gym Membership The gym has a one-time sign-up fee of \( \$ 90 \) and monthly membership dues of \( \$ 20 \). Let \( x \) represent the number of months. The function \( f(x) \) representing the total cost after \( x \) months can be expressed as: \[ f(x) = 90 + 20x \] ### d) Job Salary The job offers a starting salary of \( \$ 38,000 \) with yearly raises of \( 4\% \). Let \( x \) represent the number of years. The function \( f(x) \) representing the salary after \( x \) years can be expressed as: \[ f(x) = 38000 \cdot (1.04)^x \] ### Summary of Functions - a) \( f(x) = 60 - 3.5x \) - b) \( f(x) = 500 \cdot \left(\frac{1}{2}\right)^x \) - c) \( f(x) = 90 + 20x \) - d) \( f(x) = 38000 \cdot (1.04)^x \)