Question

(04.07) 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? (2 points)

Answer 1

Answer: Hello there!

Here we have two functions:

f(x) = 3x

g(x) = 7x + 6

We want to see in what month f(x) is bigger than g(x)

or

f(x) > g(x)

3x > 7x + 6

we can subtract 7x in both sides:

3x  - 7x > 7x + 6 - 7x

-4x > 6

Now, this means that x should be a negative number, this has no sense because if we are measuring if we put a negative number there, then we will end up with a negative number of population.

Then there is no month where f(x) is greater than g(x)

This also can be seen because g(x) has a positive intercept when g(x) has an intercept equal to zero, and because g(x) has a bigger slope, which means that grows faster than f(x) as the months passes.

Answer 2

3x> 7x+6

subtract 7x from each side

-4x > 6

divide by -4  which causes the inequality sign to flip

x < -6/4

x < 2/3

The f(x) population stops being larger in the first month