Question

Liam is using sequences to compare the growth rates of h(x)=1.2x
and j(x)=1.2x
. Which statement correctly describes how Liam should do this and what he will observe?(1 point)
Responses

Liam should look at where one sequence has terms greater than the terms in the other sequence. The growth rate of j(x)=1.2x
is only greater than the growth rate of h(x)=1.2x
when its terms are greater.
Liam should look at where one sequence has terms greater than the terms in the other sequence. The growth rate of j times x is equal to 1 point 2 to the x th power is only greater than the growth rate of h of x is equal to 1 point 2 x when its terms are greater.

Liam should compare the rates of change of the terms in both sequences. The growth rate of h(x)=1.2x
will quickly surpass the growth rate of j(x)=1.2x

Liam should compare the rates of change of the terms in both sequences. The growth rate of h of x is equal to 1 point 2 x will quickly surpass the growth rate of j times x is equal to 1 point 2 to the x th power

Liam should compare the rates of change of the terms in both sequences. The growth rate of j(x)=1.2x
will quickly surpass the growth rate of h(x)=1.2x

Liam should compare the rates of change of the terms in both sequences. The growth rate of j times x is equal to 1 point 2 to the x th power will quickly surpass the growth rate of h of x is equal to 1 point 2 x

Liam should look at where one sequence has terms greater than the terms in the other sequence. The growth rate of h(x)=1.2x
is only greater than the growth rate of j(x)=1.2x
when its terms are greater.

Answer 1

Choose the statement that says Liam should compare the rates of change of the terms in both sequences, and that j(x) = 1.2^x will (eventually) surpass h(x) = 1.2x.

Reason: j multiplies by 1.2 each step (exponential growth) while h adds 1.2 each step (linear growth), so the exponential sequence will eventually grow faster and overtake the linear sequence.