Question

1. identify the y-intercept of each of the exponential functions.

$3123(432,543)^x$ $76(89,047,832)^x$
$45(54)^x$ $r(x) = 57(3.77)^x$

Explanation:

For the function \( 3123(432,543)^x \):

Step1: Recall the y - intercept definition

The y - intercept of a function \( y = f(x) \) is the value of \( y \) when \( x = 0 \). For an exponential function of the form \( y=a(b)^x \), we substitute \( x = 0 \) into the function.

Step2: Substitute \( x = 0 \) into the function

When \( x = 0 \), we know that any non - zero number raised to the power of 0 is 1, i.e., \( (432,543)^0=1 \). So, \( y = 3123\times(432,543)^0=3123\times1 = 3123 \).

For the function \( 76(89,047,832)^x \):

Step1: Recall the y - intercept definition

The y - intercept occurs at \( x = 0 \). For the exponential function \( y = a(b)^x \), we use the property of exponents \( b^0=1 \) (where \( b
eq0 \)).

Step2: Substitute \( x = 0 \) into the function

Substitute \( x = 0 \) into \( y = 76(89,047,832)^x \). We get \( y=76\times(89,047,832)^0 \). Since \( (89,047,832)^0 = 1 \), then \( y=76\times1=76 \).

For the function \( 45(54)^x \):

Step1: Recall the y - intercept definition

The y - intercept is found by setting \( x = 0 \) in the function \( y = a(b)^x \).

Step2: Substitute \( x = 0 \) into the function

When \( x = 0 \), \( (54)^0 = 1 \). So, \( y=45\times(54)^0=45\times1 = 45 \).

For the function \( r(x)=57(3.77)^x \):

Answer:

s:

• For \( 3123(432,543)^x \), the y - intercept is \( 3123 \).
• For \( 76(89,047,832)^x \), the y - intercept is \( 76 \).
• For \( 45(54)^x \), the y - intercept is \( 45 \).
• For \( r(x)=57(3.77)^x \), the y - intercept is \( 57 \).