Question

Two separate bacteria populations grow each month and are represented by the functions f(x) = 3x and g(x) = 7x + 6. In what month is the f(x) population greater than the g(x) population?

Month 1
Month 2
Month 3
Month 4

Answer 1

To find in what month the f(x) population is greater than the g(x) population, set up an equation and solve for x. The solution is x > -6/4, which means it happens in Month 2.

Step-by-step explanation:

To find in what month the f(x) population is greater than the g(x) population, we can set up an equation and solve for x. The equation is:

3x > 7x + 6

Subtracting 7x from both sides:

-4x > 6

Dividing both sides by -4 (remember to reverse the sign):

x < -6/4

Since x represents months, we know it can't be negative, so the solution is x > -6/4. This means that the f(x) population is greater than the g(x) population in Month 2.

Answer 2

The f(x) population will never be more than the g(x) population with the given equations.

Step-by-step explanation:

Due to the fact that we have 7x in the g(x) equation and only 3x in the f(x) equation, then we know that every month, the g(x) gets larger than the f(x) by 4. Therefore, the f(x) equation will never catch the g(x) equation.