Question

1. identify the y - intercept of each of the exponential functions. \\( 3123(432,543)^x \\) \\( 76(89,047,832)^x \\)

Explanation:

To identify the \( y \)-intercept of an exponential function of the form \( y = a(b)^x \), we use the fact that the \( y \)-intercept occurs at \( x = 0 \). When \( x = 0 \), any non - zero number raised to the power of 0 is 1 (\( b^0=1 \) for \( b
eq0 \)). So the \( y \)-intercept is found by substituting \( x = 0 \) into the function.

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

Step 1: Substitute \( x = 0 \) into the function

We know that for any real number \( a\) and \( b\) (where \( b>0,b
eq1\)), when we substitute \( x = 0 \) into the exponential function \( y=a\times b^{x}\), we get \( y=a\times b^{0}\). Since \( b^{0} = 1\) (by the zero - exponent rule: \( a^{0}=1\) for \( a
eq0\)), the function becomes \( y=3123\times(432,543)^{0}\)

Step 2: Evaluate the expression

Since \( (432,543)^{0}=1\), then \( y = 3123\times1=3123\). So the \( y \)-intercept of the function \( y = 3123(432,543)^x\) is \( 3123\) (the point is \( (0,3123) \))

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

Step 1: Substitute \( x = 0 \) into the function

Substitute \( x = 0 \) into the function \( y = 76\times(89,047,832)^{x}\). We get \( y=76\times(89,047,832)^{0}\)

Step 2: Evaluate the expression

Using the zero - exponent rule (\( a^{0}=1\) for \( a
eq0\)), \( (89,047,832)^{0}=1\). Then \( y=76\times1 = 76\). So the \( y \)-intercept of the function \( y = 76(89,047,832)^x\) is \( 76\) (the point is \( (0,76) \))

Answer:

s:

• For \( y = 3123(432,543)^x \), the \( y \)-intercept is \( 3123 \) (at the point \( (0,3123) \))
• For \( y = 76(89,047,832)^x \), the \( y \)-intercept is \( 76 \) (at the point \( (0,76) \))