Question

Two different plants grow each year at different rates, which are represented by the functions f(x) = 4x and g(x) = 5x + 2. What is the first year the f(x) height is greater than the g(x) height? Year 0 Year 1 Year 2 Year 3

Answer 1

Option 1 - Year 0

Explanation:

Given : Two different plants grow each year at different rates, which are represented by the functions
`f(x) = 4x` and
`g(x) = 5x + 2`.

To find : What is the first year the f(x) height is greater than the g(x) height?

Solution :

We have given two functions
`f(x) = 4x` and
`g(x) = 5x + 2`.

According to question,

The f(x) height is greater than the g(x) height,

i.e.
`f(x)>g(x)`

`4x>5x+2`

Subtract -5x both side,

`4x-5x<5x+2-5x`

`-x<2`

Multiply both side by -1,

`x<-2`

As number of years cannot be negative.

So, The first year the f(x) height is greater than the g(x) height is year 0.

Therefore, Option 1 is correct.