Question

PLEASE HELPP TIMED

From x = 0 to x = 2, which of the following best describes the growth of the two functions below?
FIRST GRPAH IS Y=5X SECOND IS Y=5^X
A Y=5X GROWS GROWS SLOWER THAN Y=5^X
B Y=5X GROWS FASTER THAN Y=5^X
C Y=5^X GROWS AT THE SAME RATE AS Y=5X
D Y=5^X GROWS OVER A DIFFERENT INTERVAL THAN Y=5X

Answer 1

In the interval x = 0 to 2,
the 5^x graph goes from y=1 to y=25
and the 5x graph goes from y=0 to y=20

Thus,
A Y=5X GROWS GROWS SLOWER THAN Y=5^X

Answer 2

The correct option is A.

Explanation:

The given functions are

`y=5x`

`y=5^x`

The slope of a function is defined as

`m=(f(x_2)-f(x_1))/(x_2-x_1)`

In first function, at x=0

`y=5(0)=0`

At x=2

`y=5(2)=10`

Growth rate of first function is

`m_1=(10-0)/(2-0)=5`

Therefore the growth rate of y=5x is 5 from x = 0 to x = 2.

In second function, at x=0

`y=5^(0)=1`

At x=2

`y=5^(2)=25`

Growth rate of first function is

`m_1=(25-1)/(2-0)=12`

Therefore the growth rate of y=5^x is 12 from x = 0 to x = 2.

So we can say that y=5x grows slower than y=5^x.

Therefore option A is correct.