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? A. Month 1 B. Month 2 C. Month 3 D. Month 4

Answer 1

Answer:

D. Month 4

Step-by-step explanation:

We are given

Two separate bacteria populations grow each month and are represented by the functions

$f(x)=3^x$

$g(x)=7x+6$

now, we can verify each options and check which one holds f(x)>g(x)

option-A:

we can plug x=1

$f(1)=3^1=3$

$g(1)=7\times 1+6=13$

so,

$f(1)$

so, this is FALSE

option-B:

we can plug x=2

$f(2)=3^2=9$

$g(2)=7\times 2+6=20$

so,

$f(2)$

so, this is FALSE

option-C:

we can plug x=3

$f(3)=3^3=27$

$g(3)=7\times 3+6=27$

so,

$f(3)=g(3)$

so, this is FALSE

option-D:

we can plug x=4

$f(4)=3^4=81$

$g(4)=7\times 4+6=34$

so,

$f(4)>g(4)$

so, this is TRUE