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

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

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.

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.
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.

Location A will reach $2,000 in profit in about 1.4 weeks, and Location B will reach $2,000 in about 1 week.

Answer 1

To determine when each location reaches a profit of $2,000, we need to set each function equal to 2 (since the profits are given in thousands of dollars).

1. For Location A modeled by \( f(x) = 4x - 2 \):
\[
4x - 2 = 2
\]
Adding 2 to both sides:
\[
4x = 4
\]
Dividing by 4:
\[
x = 1
\]

2. For Location B modeled by \( g(x) = x^2 \):
\[
x^2 = 2
\]
Taking the square root of both sides:
\[
x = \sqrt{2} \approx 1.414
\]

Now let's summarize the results:
- Location A will reach a profit of $2,000 in about **1 week**.
- Location B will reach a profit of $2,000 in about **1.4 weeks**.

Based on these calculations, the correct response is:
**Location A will reach $2,000 in profit in about 1 week, and Location B will reach $2,000 in about 1.4 weeks.**