Question

Crystal works in sales. Every week, she earns $400 plus $50 for every sale she made that week. The longer she works in this job, the better she gets at making sales. Her weekly sales are modelled by S(t) = 3+2t sales, t weeks after she began the job. How is her weekly pay changing over time?

Answer 1

Crystal's weekly pay changes over time as represented by the linear function E(t) = 550 + 100t, where E(t) is her earnings and t is the number of weeks. For each additional week, her weekly pay increases by $100 due to the increase in sales she makes as she becomes more experienced.

Step-by-step explanation:

Crystal's weekly pay is modelled by a linear function where she earns a fixed amount plus a variable amount based on her sales. The base pay is $400 every week, and for each sale she makes, she earns an additional $50. Over time, as represented by the model S(t) = 3+2t, her weekly sales are increasing based on the number of weeks t she has been working. The number of sales she makes each week is 3 + 2t.

To find out how her weekly pay is changing over time, we can calculate her total weekly earnings based on the number of sales. Her weekly earnings E(t) can be represented by the equation E(t) = 400 + 50 × S(t), or E(t) = 400 + 50(3 + 2t). Simplifying this, we get E(t) = 400 + 150 + 100t = 550 + 100t. Therefore, her weekly pay increases by $100 for every additional week she works.