Find the x and y Intercepts y=5e^(-0.7x)

$y = 5 e^{- 0.7 x}$

Step 1

Find the x-intercepts.

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = 5 e^{- 0.7 x}$

Solve the equation.

Rewrite the equation as $5 e^{- 0.7 x} = 0$ .

$5 e^{- 0.7 x} = 0$

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln (5 e^{- 0.7 x}) = \ln (0)$

The equation cannot be solved because $\ln (0)$ is undefined.

Undefined

There is no solution for $5 e^{- 0.7 x} = 0$

No solution

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

x-intercept(s): $None$

Step 2

Find the y-intercepts.

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = 5 e^{- 0.7 \cdot 0}$

Simplify $5 e^{- 0.7 \cdot 0}$ .

Multiply $- 0.7$ by $0$ .

$y = 5 e^{0}$

Anything raised to $0$ is $1$ .

$y = 5 \cdot 1$

Multiply $5$ by $1$ .

$y = 5$

y-intercept(s) in point form.

y-intercept(s): $(0, 5)$

Step 3

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, 5)$

Step 4