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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].
1. Understand the general form of the equation: In an equation of the form [tex]\(y = a(b)^x\)[/tex], [tex]\(a\)[/tex] is the initial value when [tex]\(x = 0\)[/tex].
2. Substitute [tex]\(x = 0\)[/tex]:
[tex]\[
y = 76(1.013)^0
\][/tex]
3. Calculate [tex]\( (1.013)^0 \)[/tex]:
- Any non-zero number raised to the power of 0 is 1. So, [tex]\( (1.013)^0 = 1 \)[/tex].
4. Compute the value of [tex]\(y\)[/tex]:
[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.
1. Understand the general form of the equation: In an equation of the form [tex]\(y = a(b)^x\)[/tex], [tex]\(a\)[/tex] is the initial value when [tex]\(x = 0\)[/tex].
2. Substitute [tex]\(x = 0\)[/tex]:
[tex]\[
y = 76(1.013)^0
\][/tex]
3. Calculate [tex]\( (1.013)^0 \)[/tex]:
- Any non-zero number raised to the power of 0 is 1. So, [tex]\( (1.013)^0 = 1 \)[/tex].
4. Compute the value of [tex]\(y\)[/tex]:
[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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