Precalculus Examples

$i = 5.3 (1 - e^{- 0.22 t \cdot 0.012})$

Step 1

Simplify.

Tap for more steps...

Step 1.1

Multiply $0.012$ by $- 0.22$ .

$i = 5.3 (1 - e^{- 0.00264 t})$

Step 1.2

Divide each term in $i = 5.3 (1 - e^{- 0.00264 t})$ by $5.3$ .

$\frac{i}{5.3} = \frac{5.3 (1 - e^{- 0.00264 t})}{5.3}$

Step 1.3

Multiply by $1$ .

$\frac{1 i}{5.3}$

Step 1.4

Factor $5.3$ out of $5.3$ .

$\frac{1 i}{5.3 (1)}$

Step 1.5

Separate fractions.

$\frac{1}{5.3} \cdot \frac{i}{1}$

Step 1.6

Divide $1$ by $5.3$ .

$0.18867924 \frac{i}{1}$

Step 1.7

Divide $i$ by $1$ .

$0.18867924 i$

Step 1.8

Reduce by cancelling the common factors.

$0.18867924 i = e^{- 0.00264 t}$

Step 2

Convert the exponential equation to a logarithmic equation using the logarithm base $(e)$ of the left side $(0.18867924 i)$ equals the exponent $(- 0.00264 t)$ .

$\log_{e} (0.18867924 i) = - 0.00264 t$