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

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