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4 years ago

Asap help!!!!!! Which relations are functions? Select Function or Not a function for each graph.

Mathematics

1 answer:

Sergio [31]4 years ago

8 0

Answer:

1st Graph: Function

2nd Graph: Function

3rd Graph: Not a function

4th Graph: Not a function

Step-by-step explanation:

We can determine if a graph is a function or not using the Vertical Line Test. Since we see that 1 and 2 pass but 3 and 4 pass, 1 and 2 are functions while 3 and 4 are not.

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A bacteria culture starts with 400 bacteria and grows at a rate proportional to its size. After 4 hours, there are 9000 bacteria

Kaylis [27]

Answer:

A) The expression for the number of bacteria is $P(t) = 400e^{0.7783t}$ .

B) After 5 hours there will be 19593 bacteria.

C) After 5.55 hours the population of bacteria will reach 30000.

Step-by-step explanation:

A) Here we have a problem with differential equations. Recall that we can interpret the rate of change of a magnitude as its derivative. So, as the rate change proportionally to the size of the population, we have

$P' = kP$

where $P$ stands for the population of bacteria.

Writing $P'$ as $\frac{dP}{dt}$ , we get

$\frac{dP}{dt} = kP$ .

Notice that this is a separable equation, so

$\frac{dP}{P} = kdt$ .

Then, integrating in both sides of the equality:

$\int\frac{dP}{P} = \int kdt$ .

We have,

$\ln P = kt+C$ .

Now, taking exponential

$P(t) = Ce^{kt}$ .

The next step is to find the value for the constant $C$ . We do this using the initial condition $P(0)=400$ . Recall that this is the initial population of bacteria. So,

$400 = P(0) = Ce^{k0}=C$ .

Hence, the expression becomes

$P(t) = 400e^{kt}$ .

Now, we find the value for $k$ . We are going to use that $P(4)=9000$ . Notice that

$9000 = 400e^{k4}$ .

Then,

$\frac{90}{4} = e^{4k}$ .

Taking logarithm

$\ln\frac{90}{4} = 4k$ , so $\frac{1}{4}\ln\frac{90}{4} = k$ .

So, $k=0.7783788273$ , and approximating to the fourth decimal place we can take $k=0.7783$ . Hence,

$P(t) = 400e^{0.7783t}$ .

B) To find the number of bacteria after 5 hours, we only need to evaluate the expression we have obtained in the previous exercise:

$P(5) =400e^{0.7783*5} = 19593.723 \approx 19593$ .

C) In this case we want to do the reverse operation: we want to find the value of t such that

$30000 = 400e^{0.7783t}$ .

This expression is equivalent to

$75 = e^{0.7783t}$ .

Now, taking logarithm we have

$\ln 75 = 0.7783t$ .

Finally,

$t = \frac{\ln 75}{0.7783} \approx 5.55$ .

So, after 5.55 hours the population of bacteria will reach 30000.

6 0

4 years ago

Roses are $1.50 each and lilies are $1.25 each. Ellis spent $28.75 for 15 of the flowers. How many of each type of flower did he

sertanlavr [38]

Answer:

He could have bought 23 lilies by itself

Step-by-step explanation:

8 0

3 years ago

Tony pays $6 for a 4-pound bag of apples. <br><br> how much does tony pay per pound for apples?

hram777 [196]

Answer:

$1.50 per pound

Step-by-step explanation:

$6 for 4 lb

$6 / 4

since wanting to figure out how much 1 lb cost then divide the total by 4 since $6 is 4 lb

6 / 4 = 1.5

hope this helps

5 0

4 years ago

Read 2 more answers

Complete explanation of water the graph represents a proportional or a non-for pusher liner relationship

faust18 [17]

Answer:

Porportional

Step-by-step explanation:

Its a straight line.

5 0

3 years ago

Only 17 plz rlly need help plz bro

Airida [17]

The question GIVES us an equation:

V₀ = √(v² - 64h) .

It TELLS us that v should be 100 ft/sec and h is 150 ft.
All we have to do is plug the numbers into the equation,
and then do the arithmetic to find V₀.
There's not even any Physics to do. Only arithmetic.

V₀ = √(v² - 64h)

v = 100
h = 150

V₀ = √(100² - 64·150)

V₀ = √(10,000 - 9,600)

V₀ = √400

V₀ = 20 ft per sec .

4 0

4 years ago