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Answer :
To find the [tex]$y$[/tex]-intercept of the equation [tex]\( y = 76(1.013)^x \)[/tex], you need to determine the value of [tex]\( y \)[/tex] when [tex]\( x = 0 \)[/tex].
Here's how you do it step-by-step:
1. Identify the equation: The equation given is [tex]\( y = 76(1.013)^x \)[/tex].
2. Set [tex]\( x \)[/tex] to 0: The [tex]$y$[/tex]-intercept is defined as the value of [tex]\( y \)[/tex] when [tex]\( x = 0 \)[/tex].
3. Substitute [tex]\( x = 0 \)[/tex] into the equation:
[tex]\[
y = 76(1.013)^0
\][/tex]
4. Calculate the expression: Any number raised to the power of 0 is 1. Thus:
[tex]\[
(1.013)^0 = 1
\][/tex]
5. Multiply the result by 76:
[tex]\[
y = 76 \times 1 = 76
\][/tex]
Therefore, the [tex]$y$[/tex]-intercept of the equation is 76.
Here's how you do it step-by-step:
1. Identify the equation: The equation given is [tex]\( y = 76(1.013)^x \)[/tex].
2. Set [tex]\( x \)[/tex] to 0: The [tex]$y$[/tex]-intercept is defined as the value of [tex]\( y \)[/tex] when [tex]\( x = 0 \)[/tex].
3. Substitute [tex]\( x = 0 \)[/tex] into the equation:
[tex]\[
y = 76(1.013)^0
\][/tex]
4. Calculate the expression: Any number raised to the power of 0 is 1. Thus:
[tex]\[
(1.013)^0 = 1
\][/tex]
5. Multiply the result by 76:
[tex]\[
y = 76 \times 1 = 76
\][/tex]
Therefore, the [tex]$y$[/tex]-intercept of the equation is 76.
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