In the number 4.735 the underlined digit is 4 what number does it round to if its in the ones place

A bacteria culture starts with 160 bacteria and grows at a rate proportional to its size. After 5 hours there will be 800 bacter

Leona [35]

Answer:

Step-by-step explanation:

Let the rate at which the bacteria grow be represented by the exponential equation

P(t) = P0e^kt

P(t) is the population of the bacteria after time t

P0 is the initial population

k is the constant of variation

t is the time

If the initial Population is 160 bacteria's, them the equation becomes;

P(t) = 160e^kt

b) if After 5 hours there will be 800 bacteria, this means

at t = 5 p(t) = 800

Substitute and get k

800 = 160e^5k

800/160 = e^5k

5 = e^5k

Apply ln to both sides

Ln5 = lne^5k

ln5 = 5k

k = ln5/5

k = 0.3219

Next is to calculate the population after 7hrs i.e at t = 7

P(7) = 160e^0.3219(7)

P(7) = 160e^2.2532

P(7) = 160(9.5181)

P(7) = 1522.9

Hence the population after 7houra will be approximately 1523populations

c) To calculate the time it will take the population to reach 2790

When p(t) = 2790, t = ?

2790 = 160e^0.3219t

2790/160 = e^0.3219t

17.4375 = e^0.3219t

ln17.4375 = lne^0.3219t

2.8587 = 0.3219t

t = 2.8587/0.3219

t = 8.88 hrs

Hence it will take approximately 9hrs for the population to reach 2790

7 0

2 years ago

Write out the form of the partial fraction decomposition of the function (as in this example). Do not determine the numerical va

pentagon [3]

Answer:

The answer is " $\frac{A}{(x-2)} + \frac{B}{(x+3)}$ "

Step-by-step explanation:

Let the given value is: $\frac{x-6}{x^2+x-6}$

$\to \frac{x-6}{x^2+x-6}=\frac{x-6}{x^2+(3-2)x-6}\\\\$

$=\frac{x-6}{x^2+(3-2)x-6}\\\\ =\frac{x-6}{x^2+3x-2x-6}\\\\ =\frac{x-6}{x(x+3)-2(x+3)}\\\\ =\frac{x-6}{(x+3)(x-2)}\\\\=\frac{A}{(x-2)} + \frac{B}{(x+3)}$

3 0

2 years ago

Chris runs 6 miles in 50 minutes. At the same rate, how many miles would he run in 35 minutes?

Nataly_w [17]

You could either find how far Chris can run in 60 minutes, or write an equation of ratios:

x 35 min
--------- = --------------
6 mi 50 min

Solving for x: 50x = 210; x = 4.2 miles (answer)

4 0

3 years ago

Tania has 56 liters of milk. She uses the milk to make muffins and cakes. Each batch of muffin requires 7 liters of milk and eac

Sophie [7]

Equally divide 56 into 2 halves. 28 liters. 28 liters for muffins and 28 liters for cakes.

(muffins require 7 liters) 28÷7= 4
(cakes require 4 liters) 28÷4=7
x= 4 batches of muffins
y= 7 batches of cakes.

4 0

3 years ago

Find the volume of the cone. Use 3.14 for pi.

Andreyy89

Answer:

V = 628

Step-by-step explanation:

Formula to find volume(V) of cone:

$v = \frac{1}{3} \pi {r}^{2} h$

6 0

2 years ago