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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's how you do it:
1. Substitute [tex]\( x = 0 \)[/tex] into the equation:
[tex]\[ y = 76(1.013)^0 \][/tex]
2. Calculate [tex]\( (1.013)^0 \)[/tex]:
Any number raised to the power of 0 is always 1. So,
[tex]\[ (1.013)^0 = 1 \][/tex]
3. Calculate the [tex]\( y \)[/tex]-intercept:
[tex]\[ y = 76 \times 1 = 76 \][/tex]
Therefore, the [tex]\( y \)[/tex]-intercept of the equation is 76.
1. Substitute [tex]\( x = 0 \)[/tex] into the equation:
[tex]\[ y = 76(1.013)^0 \][/tex]
2. Calculate [tex]\( (1.013)^0 \)[/tex]:
Any number raised to the power of 0 is always 1. So,
[tex]\[ (1.013)^0 = 1 \][/tex]
3. Calculate the [tex]\( y \)[/tex]-intercept:
[tex]\[ y = 76 \times 1 = 76 \][/tex]
Therefore, the [tex]\( y \)[/tex]-intercept of the equation is 76.
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