Question

mathematics i a-g cr sem a aguirre
vertical stretches and shrinks of exponential function
an exponential function is shown.
$y = 5(2.5)^x$
what are the growth factor and initial value of the function?
enter your answers in the boxes.
growth factor:
initial value:

Explanation:

Step1: Recall exponential function form

The general form of an exponential function is \( y = a(b)^x \), where \( a \) is the initial value and \( b \) (with \( b>0, b
eq1 \)) is the growth or decay factor. If \( b > 1 \), it's a growth factor.

Step2: Identify growth factor and initial value

For the function \( y = 5(2.5)^x \), comparing with \( y = a(b)^x \), we have \( a = 5 \) (initial value) and \( b = 2.5 \) (growth factor, since \( 2.5>1 \)).

Answer:

Growth factor: \( 2.5 \)
Initial value: \( 5 \)