I need to round 16,500 nearest thousand feet

A chemical substance has a decay rate of 6.9% per day. The rate of change of an amount N of the chemical is given by the equatio

GaryK [48]

Answer:

a) $N=N_0e^{-0.069t}$

b) $N=696.9$ grams

c) $t=10$ days

Step-by-step explanation:

a)

We are going to use separation of variables to solve.

Get all your t's to one side and your N's to opposing side.

$\frac{dN}{dt}=-0.069N$

Multiply both sides by $dt$ :

$dN=-0.069N dt$

Divided both sides by $N$ :

$\frac{dN}{N}=-0.069 dt$

Integrate both sides:

$\ln|N|=-0.069t+C$

The equivalent exponential form is:

$e^{-0.069t+C}=N$

Using law of exponents you can write this as:

$e^{-0.069t}e^C=N$

$e^C$ is just a positive constant that I'm going to replace with K:

$e^{-0.069t}K=N$

Applying the symmetric property of equality:

$N=e^{-0.069t}K$

Applying the commutative property of multiplication:

$N=Ke^{-0.069t}$

K actually represents the initial amount of chemical substance since when plugging in 0 for t you get K for N, like so:

$N=Ke^{-0.069 \cdot 0}$

$N=Ke^{0}$

$N=K(1)$

$N=K$

We are given at time 0 the amount of chemical substance,N, is K. They want us to represent this value with $N_0$ instead. So the exponential equation is:

$N=N_0e^{-0.069t}$

b)

We are given $N_0=800$ at $t=0$ .

We are asked to find how much of the chemical substance, N, remains after 2 days. So we replace t with 2 in $N=800e^{-0.069t}$ :

$N=800e^{-0.069 \cdot 2}$

Put into calculator:

$N=696.9$ (this was rounded to the nearest tenths)

c)

The last part is asking for how many days will it take a initial 800 grams to go down to half of 800 grams.

We need to see the following equation:

$\frac{1}{2}(800)=800e^{-0.069t}$

$400=800e^{-0.069t}$

Divide both sides by 800:

$\frac{400}{800}=e^{-0.069t}$

Reduce the fraction:

$\frac{1}{2}=e^{-0.069t}$

Convert to logarithmic form:

$\ln(\frac{1}{2})=-0.069t$

Divide both sides by -0.069:

$\frac{\ln(\frac{1}{2})}{-0.069}=t$

Input into calculator:

$10.0=t$

$t=10.0$

$t=10$

6 0

4 years ago

Which table has a constant of proportionality between y and x of 0.9? someone plz answer if i dont get this i wont be able to ge

Tems11 [23]

Answer:

B

Step-by-step explanation:

3 0

4 years ago

Write 23/6 as a mixed number

natali 33 [55]

3 5/6
Youre welcomeeeeeeeee

5 0

3 years ago

Read 2 more answers

Which inequality is represented by the graph

DanielleElmas [232]

Answer:

y ≥ -2x + 2.5

Step-by-step explanation:

It's kind of hard to tell because no points are given on the graph, but we can first find the b value of 2.5 in the equation y = mx +b as it is the y-intercept.

Using that value, we can also recognize that at one, it looks like the y-value is .5. using our slope formula (change in y / change in x), we can plug in the two points of (0, 2.5) and (1, 0.5) to get a slope of -2.

Now that we have our equation, we can make it an inequality!

Since the graph is shaded upwards, we know it is going to be a greater than symbol, and since the line itself solid and not dotted, we know that the points on the line are also solutions, meaning that it is also equal to the line

Hence, we get the ≥ sign.

Putting it all together, we get our final equation of y ≥ -2x + 2.5 ! :))

6 0

3 years ago

Cody was 165cm tall on the first day of school this year, which was 10% taller than he was on the first day of school last year.

klemol [59]

Answer: 148.5

Step-by-step explanation:

well there is no real question here but cody is 165 which means you have to multiply that by 10% or 0.10 which gives you 16.5 and subtract that from the total

4 0

3 years ago