Answer :

To find the [tex]\( y \)[/tex]-intercept of the equation [tex]\( y = 76(1.013)^x \)[/tex], we need to determine the value of [tex]\( y \)[/tex] when [tex]\( x = 0 \)[/tex].

Here are the steps you follow to find the [tex]\( y \)[/tex]-intercept:

1. Identify what the [tex]\( y \)[/tex]-intercept means: The [tex]\( y \)[/tex]-intercept of a function is the value of [tex]\( y \)[/tex] when the input [tex]\( x \)[/tex] is zero. It is the point where the graph of the equation intersects the [tex]\( y \)[/tex]-axis.

2. Substitute [tex]\( x = 0 \)[/tex] into the equation:
In the given equation [tex]\( y = 76(1.013)^x \)[/tex], replace [tex]\( x \)[/tex] with 0. So, it becomes:
[tex]\[
y = 76(1.013)^0
\][/tex]

3. Calculate the expression [tex]\( (1.013)^0 \)[/tex]:
Any number raised to the power of 0 is 1. So, [tex]\( (1.013)^0 = 1 \)[/tex].

4. Complete the calculation:
Substitute back into the equation:
[tex]\[
y = 76 \times 1 = 76
\][/tex]

Therefore, the [tex]\( y \)[/tex]-intercept of the equation [tex]\( y = 76(1.013)^x \)[/tex] is 76.

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