How to solve division with exponents

1 answer:

5 0

In division, exponents with the same base are subtracted.
example:
$\frac{x^4}{x^2} = x^2 \\ \\ \frac{ x^{3} y^{2} }{ x^{6} y} = \frac{y}{ x^{3} } \\ \\ Negative-exponents \\ \\ x^{-2} = \frac{1}{ x^{2} }$

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zheka24 [161]

SOLUTION

We have been given the equation of the decay as

$\begin{gathered} N=N_0e^{-kt} \\ where\text{ } \\ N_0=initial\text{ amount of C-14 at time t} \\ N=amount\text{ of C-14 at time t = 65\% of N}_0=0.65N_0 \\ k=0.0001 \\ t=time\text{ in years = ?} \end{gathered}$

So we are looking for the time

Plugging the values into the equation, we have

$\begin{gathered} N=N_0e^{-kt} \\ 0.65N_0=N_0e^{-0.0001t} \\ e^{-0.0001t}=\frac{0.65N_0}{N_0} \\ e^{-0.0001t}=0.65 \end{gathered}$

Taking Ln of both sides, we have

$\begin{gathered} ln(e^{-0.000t})=ln(0.65) \\ -0.0001t=ln(0.65) \\ t=\frac{ln(0.65)}{-0.0001} \\ t=4307.82916 \end{gathered}$

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pishuonlain [190]

You have that:

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Bogdan [553]

Answer:

$\boxed{\bold{z=-60}}$