Decay can be represented by the equation $A=A_0e^{rt}$ . We can find the rate at which it decays by using t=3 hours and A=3000. This means $A_0=6000$ in this context.

$A=A_0e^{rt}\\3000=6000e^{r(3)}$

$0.5=e^{(24.5)r}$

After substituting, we divided by 6000 to each side to get 0.5 on the left. Now to solve for r, we will take the natural log of both sides and use log rules to isolate r.

$ln 0.5=ln e^{(3)r}\\ln 0.5=3r (ln e)\\\frac{ln0.5}{3} =r$

We know $lne=1$ so we were able to cancel it out and divide both sides by 3.

We solve with a calculator $\frac{ln0.5}{3} =r\\-0.23=r$

We change -0.23 into a percent by multiplying by 100 to get -23% as the rate.

The equation is $A=6000e^{-0.23t}$

5 0

3 years ago

Seven fifths of a number, z, subtracted from 6 times the same number is 3 .

Alex_Xolod [135]

6z-7z/5=3

(30z-7z)/5=3

30z-7z=15

23z=15

z=15/23

8 0

3 years ago

Katy buys 4 DVDs every 2 weeks how many will she buy in 10

malfutka [58]

If she maintains her average amount of movies bought every week, then she will buy 20 DVDs in 10 weeks. Explanation: she buys 4 every week, so if we want to find out how many are in 10 weeks, we must multiply two until we get to 10 ( five weeks ) then multiply that buy her average of movies. And that is how we get the answer of 20 DVDs! ( her at least I did )

Anyways, hope this helps!

5 0

3 years ago

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