Question

Two separate bacteria populations that grow each month at different rates are represented by the functions f(x) and g(x). In what month does the f(x) population exceed the g(x) population? Month (x) f(x) = 3x g(x) = 7x + 6 1 3 13 2 9 20 Month 3 Month 4 Month 5 Month 6

Answer 1

Answer: month 4

Step-by-step explanation

ill try to explain this as simple and short as possible

our equations are

f(x) = 3x   and   g(x) = 7x + 6

we need to see which one grows faster per month. so all you do is plug in the number of months into X in each equation then solve. once you have an answer, plug in the next number of months til you have an answer

we already have the first and second months of each equation so now you just do the next four

for f(x) the growth per month is this

1 month = 3

2 months =9

3 months =27

4 months =81

5 months = 243

and 6 = 729

good, next we for g(x) we plug in the number of months and we get

1 month= 13

2 month = 20

3= 27

4= 34

5= 41

6= 48

SO f(x) starts growing exponentially faster than g(x) during the 4th month, because that's when it starts increasing faster

hope this wasn't too complex, sorry its so long

Answer 2

Step-by-step explanation:

This is confusing, what does g(x) equal? There's a bunch of random numbers there. I'll just assume.

They stated that f(x) needs to exceed g(x), so make an inequality plugging in the values

$3x > 7x + 6$

You see, function f(x) needs to be higher than function g(x)

Subtract 7x from both sides to get:

$- 4x > 6$

Divide both sides by -4, when you divide by a negative number the signs switch so it is now less than.

x < -1.5

And obviously that's not an answer up there, so you made a mistake stating the values of the functions