Question

A snow cone company owns two locations in town and wants to compare their weekly profits. The function f(x)=4x−2
gives Location A’s profits in thousands of dollars after x weeks. The function g(x)=x2
gives Location B’s profits in thousands of dollars after x weeks. Using GeoGebra to model these two situations, when will each company have a profit of $2,000?(1 point)
Responses

Location A will reach $2,000 in profit in about 1.4 weeks, and Location B will reach $2,000 in about 1 week.
Location A will reach $2,000 in profit in about 1.4 weeks, and Location B will reach $2,000 in about 1 week. - no response given

Location A will reach $2,000 in profit in about 1 week, and Location B will reach $2,000 in about 1.4 weeks.
Location A will reach $2,000 in profit in about 1 week, and Location B will reach $2,000 in about 1.4 weeks. - no response given

Both companies make $2,000 in less than a week.
Both companies make $2,000 in less than a week. - incorrect

Location A will reach $2,000 in profit in about 5.5 weeks, and Location B will reach $2,000 in about 44.7 weeks.

Answer 1

Convert $2,000 to thousands: 2.

Location A: 4x − 2 = 2 → 4x = 4 → x = 1 week.

Location B: x^2 = 2 → x = √2 ≈ 1.4 weeks.

So the correct response is: Location A ≈ 1 week, Location B ≈ 1.4 weeks.