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3 years ago

Please answer this thanks

Mathematics

1 answer:

Arlecino [84]3 years ago

7 0

Answer:

$66.24

Step-by-step explanation:

TIP:

55.20 x 0.15 = 8.28

TAX:

55.20 x 0.05 = 2.76

Answer:

55.20 + 8.28 + 2.76 = 66.24

(Also always tip your server 20% unless they were bad)

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A bacteria culture starts with 660 bacteria and grows at a rate proportional to its size. After 6 hours there will be 3960 bacte

scoray [572]

Answer:

a) $P(t) = 660 e^{\frac{ln(6)}{6} t}$

b) $P(t=3) = 660 e^{\frac{ln(6)}{6}*3} = 1616.663 \approx 1617$

Step-by-step explanation:

For this case we have the following info:

$P(0) = 660$ represent the initial amount of bacteria

$P(6) = 3960$ represent the population of bacteria after 6 hours

Part a

For this case we use the proportional model given by:

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

Where P represent the population at time t and k is a constant of proportionality.

We can rewrite the model like this:

$\frac{dP}{P} = k dt$

And if we integrate both sides we got:

$ln |P|= kt + C$

Now if we apply exponential we got:

$P = e^{kt +c}= e^{kt} e^C$

$P(t)= P_o e^{kt}$

For this case using the initial condition:

$660 = P_o e^{0k}, P_o = 660$

We have the following model:

$P(t) = 660 e^{kt}$

Using the second condition $P(6) = 3960$ we have this:

$3960 = 660e^{6k}$

We can divide both sides by 660 and we got:

$6= e^{6k}$

Now we can apply natural log on both sides and we got:

$ln (6)= 6k$

$k = \frac{ln(6)}{6}=0.2986265782$

So then the model would be given by:

$P(t) = 660 e^{\frac{ln(6)}{6} t}$

Part b

For this case we just need to replace t=3 into the model and we got:

$P(t=3) = 660 e^{\frac{ln(6)}{6}*3} = 1616.663 \approx 1617$

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The monthly profit for a small company that makes long-sleeve T-shirts depends on the price per shirt. If the price is too high,

Andrej [43]

Answer:

A. $18

B. $200

C. $p\in (16,20)$

Step-by-step explanation:

Function:

$f(p) = -50p^2 + 1,800p - 16,000$

<u>Parts A and B:</u>

The price that generates the maximum profit is ate vertex of parabola. Find the coordinates of the vertex:

$p_v=\dfrac{-b}{2a}=\dfrac{-1,800}{2\cdot (-50)}=\dfrac{1,800}{100}=18\\ \\f(p_v)=-50\cdot 18^2+1,800\cdot 18-16,000=200$

The price that generates the maximum profit is $18

The maximum profit is $200

The company breaks even when the profit is positive. From the graph of the function you can see that the graph of the function is over p-axis for all $p\in (16,20)$ , so the positive profit is for $p\in (16,20)$

In p=16 and p=20, the profit is 0 and when p<16 and p>20, there will be a loss.

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4 years ago