Question

Select the TRUE statements.

Answer 1

Answer:

a) For the function $48(1.25)^x$, the parameter for the growth factor is 1.25

c) For the function $28(0.5)^x$, the parameter for the decay factor is 50%.

d) For the function y = 18x + 72, the parameter for the average rate of change is 18.

Step-by-step explanation:

We are given the following in the question:

a) the parameter for the growth factor is 1.25.

$f(x) = 48(1.25)^x$

Comparing it to

$y(x) = a(1+r)^x$

The growth factor is

$1+r = 1.25$

Thus, the given statement is true

b) the parameter for the beginning value is 75.

We are given the equation

$f(x) = 75x + 250$

The beginning value is given when x = 0. Putting value, we get

$f(0) = 75(0) + 250 = 250$

Thus, the beginning value is 250.

Hence, the given statement is false.

c) the parameter for the decay factor is 50%.

$f(x) = 28(0.5)^x$

Comparing it to

$y(x) = a(1-r)^x$

The growth factor is

$1-r = 0.5 = 50\%$

Thus, the given statement is true

d) the parameter for the average rate of change is 18.

$y = 18x + 72$

Comparing to general form of equation:

$y = mx + c$

where m is the slope and gives the average rate of change.

Thus, the average rate of change is 18.

Hence, the given statement is true.