Four student spent $12 on school lunchat this rate find amount 10 students would spend on the same school lunch

A population of bacteria is initially 6000. After three hours the population is 3000. If this rate of decay continues, find the

serious [3.7K]

Answer:

The equation is $A=6000e^{-0.23t}$ at a rate of -23%.

Step-by-step explanation:

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

2 years ago

Find the area of the isosceles trapezoid. leave your answer in simplest radical form 4cm 7cm 3cm

nata0808 [166]

The area of a trapezoid is (a+b)/2 * h
a is the length of the small base which is the one on the top and is 4cm
b is the length of the big base which is the one at the bottom and is 4 + 3 + 3 = 10cm
h is the height which is 7cm
So the area is (4+10)/2 * 7
A= 14/2 * 7
A= 7 * 7
A= 49 cm^2

8 0

3 years ago

A model ship has a mast that is 7 inches tall. A right triangular sail goes from the top of the mast to 1 inch from the bottom o

dezoksy [38]

Answer:

12 square inches.

Step-by-step explanation:

Please consider the complete question.

A model ship has a mast that is 7 inches tall. A right triangular sail goes from the top of the mast to 1 inch from the bottom of the mast. The length of the base of the sail is 4 inches. The height of the sail is along the mast. Find the area of the sail.

The sail will form a right triangle with respect to mast, whose height is 6 inches and base is 4 inches as shown in the diagram.

The area of the sail will be equal to area of triangle.

$\text{Area of triangle}=\frac{1}{2}(\text{Base}\times\text{Height})$

$\text{Area of triangle}=\frac{1}{2}(4\text{ in}\times6 \text{in})$

$\text{Area of triangle}=2\text{ in}\times 6 \text{in})$

$\text{Area of triangle}=12 \text{ in}^2$

Therefore, the area of the sail is 12 square inches.

6 0

2 years ago

At the grocery, peaches cost $2.60 per pound. Grace bought 2.3 pounds of peaches.

brilliants [131]

The total cost would be $5.98
hope this helps! :)

3 0

2 years ago

The cost of renting ice skates at a skating rink is $1.25. The rink charges $3.25 for each hour, x, of skating. Which graph best

posledela

Answer:

A

Step-by-step explanation:

Since the total cost at first will not be 5 exactly, it will turn to 4.5 (4.50). And it will be just below the five, at the first hour. And then from there, just add 3.25 each hour and forget about the 1.25 since 1.25 is used for the beginning only, and not the rest.

-By Shamaria Vaughn.

4 0

2 years ago

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