Solve for t y=350(1+0.75)^t

$y = 350 {(1 + 0.75)}^{t}$

Step 1

Rewrite the equation as $350 {(1 + 0.75)}^{t} = y$ .

$350 {(1 + 0.75)}^{t} = y$

Step 2

Add $1$ and $0.75$ .

$350 \cdot {1.75}^{t} = y$

Step 3

Divide each term in $(350 \cdot {1.75}^{t}) = y$ by $350$ and simplify.

Divide each term in $(350 \cdot {1.75}^{t}) = y$ by $350$ .

$\frac{(350 \cdot {1.75}^{t})}{350} = \frac{y}{350}$

Simplify the left side.

Cancel the common factor of $350$ .

Cancel the common factor.

$\frac{350 \cdot {1.75}^{t}}{350} = \frac{y}{350}$

Divide ${1.75}^{t}$ by $1$ .

${1.75}^{t} = \frac{y}{350}$

Step 4

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

$\ln ({1.75}^{t}) = \ln (\frac{y}{350})$

Step 5

Expand $\ln ({1.75}^{t})$ by moving $t$ outside the logarithm.

$t \ln (1.75) = \ln (\frac{y}{350})$

Step 6

Divide each term in $t \ln (1.75) = \ln (\frac{y}{350})$ by $\ln (1.75)$ and simplify.

Divide each term in $t \ln (1.75) = \ln (\frac{y}{350})$ by $\ln (1.75)$ .

$\frac{t \ln (1.75)}{\ln (1.75)} = \frac{\ln (\frac{y}{350})}{\ln (1.75)}$

Simplify the left side.

Cancel the common factor of $\ln (1.75)$ .

Cancel the common factor.

$\frac{t \ln (1.75)}{\ln (1.75)} = \frac{\ln (\frac{y}{350})}{\ln (1.75)}$

Divide $t$ by $1$ .

$t = \frac{\ln (\frac{y}{350})}{\ln (1.75)}$