Question

Gina opens a small store. Each day her store is open, her profit increases by approximately 500. Construct a function that represents the total profit after x days, explain the type of function you created and why.

a) Profit(x) = 500x; This is a linear function because the profit increases by a constant amount each day.
b) Profit(x) = x^2; This is a quadratic function because the profit grows quadratically.
c) Profit(x) = log(x); This is a logarithmic function because the profit increases slowly at first and then more rapidly.
d) Profit(x) = e^x; This is an exponential function because the profit grows exponentially with each day.

Answer 1

The function Profit(x) = 500x is a linear function that represents the daily profit increase of Gina's store by a consistent 500 dollars per day.

Step-by-step explanation:

The function that best represents the total profit after x days given that Gina's store's profit increases by approximately 500 each day would be Profit(x) = 500x. This is a linear function because the rate of increase in profit is constant for every additional day the store is open. By defining this relationship as a linear one, we are stating that the profit does not increase by a percentage each day (which would be exponential), nor does it increase at a changing rate (which would be quadratic or logarithmic). The slope, in this case, is 500, representing the consistent increase in profits per day, and the y-intercept would be 0, assuming that the store starts with no profit before it opens.