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3 years ago

Use the given conditions to write an equation for the line in point-slope form and general form,

Mathematics

1 answer:

Sveta_85 [38]3 years ago

8 0

Answer:

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Step-by-step explanation:

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Bt= 8500 *(8/27)^t/3After a special medicine is introduced into a Petri dish full of bacteria, the number of bacteria remaining

ozzi

Answer:

Every 1.71 seconds, the bacteria loses $\frac{1}{2}$

Step-by-step explanation:

Given

$B(t) = 8500 * (\frac{8}{27})^\frac{t}{3}\\$

Required [Missing from the question]

Every __ seconds, the bacteria loses $\frac{1}{2}$

First, we model the function from t/3 to t.

$B(t) = 8500 * (\frac{8}{27})^\frac{t}{3}\\$

Apply law of indices

$B(t) = 8500 * (\frac{8^\frac{1}{3}}{27^\frac{1}{3}})^t$

Evaluate each exponent

$B(t) = 8500 * (\frac{2}{3})^t$ --- This gives the number of bacteria at time t

At time 0, we have:

$B(0) = 8500 * (\frac{2}{3})^0$

$B(0) = 8500 * 1$

$B(0) = 8500$

Let r be the time 1/2 disappears.

When 1/2 disappears, we have:

$B(r) = \frac{B(0)}{2}$

$B(r) = \frac{8500}{2}$

$B(r) = 4250$

So, we have:

$B(t) = 8500 * (\frac{2}{3})^t$

Substitute r for t

$B(r) = 8500 * (\frac{2}{3})^r$

Substitute $B(r) = 4250$

$4250 = 8500 * (\frac{2}{3})^r$

Divide both sides by 8500

$\frac{4250}{8500} = (\frac{2}{3})^r$

$\frac{1}{2} = (\frac{2}{3})^r$

Take log of both sides

$log(\frac{1}{2}) = log (\frac{2}{3})^r$

Apply law of logarithm

$log(\frac{1}{2}) = r\ log (\frac{2}{3})$

Make r the subject

$r = log(\frac{1}{2}) / log (\frac{2}{3})$

$r = \frac{-0.3010}{-0.1761}$

$r = 1.71$

<em>Hence, it reduces by 1/2 after every 1.71 seconds</em>

6 0

3 years ago

Please answer my question <br> I WILL MARK BRANLIEST, AND ANSWER ONE OF YOUR QUESTIONS!!!!

ankoles [38]

Answer:

y = (4/3)x - 50

Step-by-step explanation:

Step 1 :

Identify the independent and dependent variables.

The independent variable (x) is the square footage of floor space.

The dependent variable (y) is the monthly rent.

Step 2 :

Write the information given in the problem as ordered pairs.

The rent for 600 square feet of floor space is $750 :

(600, 750)

The rent for 900 square feet of floor space is $1150 :

(900, 1150)

Step 3 :

Find the slope.

m = (y₂ - y₁) / (x₂ - x₁)

Substitute (600, 750) for (x₁, y₁) and (900, 1150) for (x₂, y₂).

m = (1150 - 750) / (900 - 600)

m = 400 / 300

m = 4/3

Step 4 :

Find the y-intercept.

Use the slope 4/3 and one of the ordered pairs (600, 750).

Slope-intercept form :

y = mx + b

Plug m = 4/3, x = 600 and y = 750.

750 = (4/3)(600) + b

750 = (4)(200) + b

750 = 800 + b

-50 = b

Step 5 :

Substitute the slope and y-intercept.

Slope-intercept form

y = mx + b

Plug m = 4/3 and b = -50

y = (4/3)x + (-50)

y = (4/3)x - 50

7 0

4 years ago

Read 2 more answers

Julie has been offered two jobs. The first pays $400 per week. The second job pays $175 per week plus 15% commission on her sale

noname [10]

So we solve for 1 week and set them equal to each other

first job pay=second job pay
400=175+15%ofsales
x=number of sales
400=175+0.15x
solve for x
subtract 175 from both sides
225=0.15x
divide both sides by 0.15
1500=x

she has to earn $1500 in sales per week to have as much as the other job

6 0

3 years ago

Read 2 more answers

Vertical and horizontal asymptotes

Ket [755]

Vertical: x=-1 and 2
Horizontal: y=-1

3 0

3 years ago

Given the distance between (x,1) and (-2,5) is 2 root 7, find the the value of x. Leave your answer in simplified exact form

Neporo4naja [7]

Answer:

Step-by-step explanation:

Distance = the square root of (x2-x1)2 + (y2-y1)2Added:Distance Formula: Given the two points (x1, y1) and (x2, y2), the distance between these points is given by the formula:square root of x2-x1 squared +y2-y1 squared

8 0

3 years ago