Find the x and y Intercepts f(x)=-4*(0.3)^x+1

$f (x) = - 4 \cdot {(0.3)}^{x} + 1$

Step 1

Find the x-intercepts.

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

$0 = - 4 \cdot {(0.3)}^{x} + 1$

Solve the equation.

Rewrite the equation as $- 4 \cdot {0.3}^{x} + 1 = 0$ .

$- 4 \cdot {0.3}^{x} + 1 = 0$

Subtract $1$ from both sides of the equation.

$- 4 \cdot {0.3}^{x} = - 1$

Divide each term in $(- 4 \cdot {0.3}^{x}) = - 1$ by $- 4$ and simplify.

Divide each term in $(- 4 \cdot {0.3}^{x}) = - 1$ by $- 4$ .

$\frac{(- 4 \cdot {0.3}^{x})}{- 4} = \frac{- 1}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 \cdot {0.3}^{x}}{- 4} = \frac{- 1}{- 4}$

Divide ${0.3}^{x}$ by $1$ .

${0.3}^{x} = \frac{- 1}{- 4}$

Simplify the right side.

Dividing two negative values results in a positive value.

${0.3}^{x} = \frac{1}{4}$

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

$\ln ({0.3}^{x}) = \ln (\frac{1}{4})$

Expand $\ln ({0.3}^{x})$ by moving $x$ outside the logarithm.

$x \ln (0.3) = \ln (\frac{1}{4})$

Divide each term in $x \ln (0.3) = \ln (\frac{1}{4})$ by $\ln (0.3)$ and simplify.

Divide each term in $x \ln (0.3) = \ln (\frac{1}{4})$ by $\ln (0.3)$ .

$\frac{x \ln (0.3)}{\ln (0.3)} = \frac{\ln (\frac{1}{4})}{\ln (0.3)}$

Simplify the left side.

Cancel the common factor of $\ln (0.3)$ .

Cancel the common factor.

$\frac{x \ln (0.3)}{\ln (0.3)} = \frac{\ln (\frac{1}{4})}{\ln (0.3)}$

Divide $x$ by $1$ .

$x = \frac{\ln (\frac{1}{4})}{\ln (0.3)}$

x-intercept(s) in point form.

x-intercept(s): $(\frac{\ln (\frac{1}{4})}{\ln (0.3)}, 0)$

Step 2

Find the y-intercepts.

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

$y = - 4 \cdot {(0.3)}^{0} + 1$

Solve the equation.

Remove parentheses.

$y = - 4 \cdot {0.3}^{0} + 1$

Remove parentheses.

$y = - 4 \cdot {(0.3)}^{0} + 1$

Simplify $- 4 \cdot {(0.3)}^{0} + 1$ .

Simplify each term.

Anything raised to $0$ is $1$ .

$y = - 4 \cdot 1 + 1$

Multiply $- 4$ by $1$ .

$y = - 4 + 1$

Add $- 4$ and $1$ .

$y = - 3$

y-intercept(s) in point form.

y-intercept(s): $(0, - 3)$

Step 3

List the intersections.

x-intercept(s): $(\frac{\ln (\frac{1}{4})}{\ln (0.3)}, 0)$

y-intercept(s): $(0, - 3)$

Step 4

Find the x and y Intercepts f(x)=-4*(0.3)^x+1

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