Question

9.) Find t in this equation

Answer 1

ANSWER
To three decimal places,
t ≈ 815.467

Step-by-step explanation


`\begin{aligned} (1)/(2) &= 1 \cdot e^(-.00085\cdot t) \\ (1)/(2) &= e^(-.00085\cdot t) \end{aligned}`

We can use the definition of logarithm to convert this equation into exponential form.


`e^a = b \iff \log_e(b) = a \iff \ln(b) = a`

therefore,


`\begin{aligned} (1)/(2) &= e^(-.00085\cdot t) \\ \ln\left( \tfrac{1}{2} \right) &= -.00085\cdot t \\ t &= \frac{\ln\left( \tfrac{1}{2} \right)}{-.00085} \\ t &\approx 815.467 \end{aligned}`

Answer 2

`(1)/(2) = e^(-0.00085t) \\ \\ ln((1)/(2)) = ln(e^(-0.00085t)) \\ \\ ln((1)/(2))= - 0.00085t \\ \\ t = (ln((1)/(2)))/(-0.00085) = 815.47`