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3 years ago

CAN SOMEONE PLEASE HELP ME WITH THESE PEOPLE

Mathematics

1 answer:

vazorg [7]3 years ago

4 0

Inverse of $f(x)=x+2$ is $f^{-1}(x)=x-2$ because

$f(x)=x+2\Rightarrow x=f^{-1}(x)+2\Rightarrow\boxed{f^{-1}(x)=x-2}$

Now $f^{-1}(-5)=-5-2=\boxed{-7}$ .

Hope this helps.

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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

3 years ago

there are d horses in a field there are 16 more female horses than male horses of the horses in the field only 25% of the male h

Oduvanchick [21]

Use f and m for "female" and "male." Then f = m + 16, and f + m = d (total)

So now we have the system of linear equations

f = m + 16
f + m = d

We can eliminate f by subst. m + 16 for f in the second equation:
d-16
m + 16 + m = d, or 2m + 16 = d. Find m. 2m = d - 16, so that m = --------
2

Assuming that the male horses are either brown or black, and that 25% of these are brown, then the rest must be black. This number is

d-16
0.75 [ --------- ] .
2

6 0

3 years ago

Help!! what 2 numbers have a sum of -1 & multiply to make -12. I know the question is simple but I just can't work it out. P

Sholpan [36]

The answer is -4 and 3 because -4 + 3 = -1 and -4 × 3 = -12. I hope this helps!

8 0

3 years ago

Find the least whole number that can replace _ to make the statement true<br><br> _ ÷ 7 > 800

Sloan [31]

7 goes into 6,300 900 times so your answer is 6,300

3 0

3 years ago