Answer :
To find the [tex]$y$[/tex]-intercept of the equation
[tex]$$
y = 76 \cdot (1.013)^x,
$$[/tex]
we need to determine the value of [tex]$y$[/tex] when [tex]$x = 0$[/tex]. The [tex]$y$[/tex]-intercept is the point where the graph crosses the [tex]$y$[/tex]-axis.
Step 1: Substitute [tex]$x = 0$[/tex] into the equation:
[tex]$$
y = 76 \cdot (1.013)^0.
$$[/tex]
Step 2: Recall that any nonzero number raised to the power [tex]$0$[/tex] is [tex]$1$[/tex]. Therefore,
[tex]$$
(1.013)^0 = 1.
$$[/tex]
Step 3: Multiply the coefficient by [tex]$1$[/tex]:
[tex]$$
y = 76 \cdot 1 = 76.
$$[/tex]
Thus, the [tex]$y$[/tex]-intercept of the equation is [tex]$76$[/tex].
[tex]$$
y = 76 \cdot (1.013)^x,
$$[/tex]
we need to determine the value of [tex]$y$[/tex] when [tex]$x = 0$[/tex]. The [tex]$y$[/tex]-intercept is the point where the graph crosses the [tex]$y$[/tex]-axis.
Step 1: Substitute [tex]$x = 0$[/tex] into the equation:
[tex]$$
y = 76 \cdot (1.013)^0.
$$[/tex]
Step 2: Recall that any nonzero number raised to the power [tex]$0$[/tex] is [tex]$1$[/tex]. Therefore,
[tex]$$
(1.013)^0 = 1.
$$[/tex]
Step 3: Multiply the coefficient by [tex]$1$[/tex]:
[tex]$$
y = 76 \cdot 1 = 76.
$$[/tex]
Thus, the [tex]$y$[/tex]-intercept of the equation is [tex]$76$[/tex].
