Question

ATTENTION PLEASE HELP ANYONE

Which statement best describes the growth rates of the functions below?
FIRST GRAPH IS Y=4X^2 SECOND GRAPH IS Y=4^X
AThe quadratic function grows faster than the exponential function over the entire interval; 0 B The exponential function grows faster than the quadratic function over the entire interval; 0 C The exponential function grows faster than the quadratic function over only one interval; 2 D The exponential function grows faster than the quadratic function over two intervals; 2

Answer 1

well, the growth rate would be the slope
the one with x=4 and y=64 would be the y=4x^2
and the one with x=4 and y=256 would be the y=x^4

one way is to find the slope between each point
but that isn't the surest way
I thin that's what they want since they want intervals, maybe

from x=0 to x=1, they have same grouth rate
from x=1 to x=2, same
from x=2 to x=3, y=4^x grows faster (slope of 48 vs 20)
from x=3 to x=4, y=4^x grows faster (slope of 192 vs 28)


so expponential function grows faster than quadratic over 2 invervals (which is 2 to 3 and 3 to 4)

Answer 2

D: The exponential function grows faster than the quadratic function over two intervals

Explanation:

From the table

The value of y is same for both functions

For first graph y=4x^2

When x= 3, y = 36

when x= 4 , y = 64

for second graph y = 4^x

When x= 3, y = 64

when x= 4 , y = 256

we can see that second graph increases faster over intervals 2 to 3 and 3 to 4

Second graph is exponential function

So, The exponential function grows faster than the quadratic function over two intervals