A bacteria culture is initially 10 grams at t=0 hours and grows at a rate proportional to its size. After an hour the bacteria culture weighs 11 grams. At what time will the bacteria have tripled in size?

Answers

Answer 1

Answer:

A bacteria culture is initially 10 grams at t=0 hours & grows at a rate proportional to its size , After an hour the bacteria culture weighs 11 grams , The bacteria takes 11.56 hours to have tripled in size.

To find the time of bacteria when increasing the growth to tripled.

Given : when time=0 hours , weight=10 grams.

when time=1 hours , weight=11 grams.

To find: when time= ? hours , weight=30grams.

Here according to question, initial size = 10 grams we have asked for tripled in size i.e. 30 grams.

Now we knows that,

The formula for exponential growth in population or size is

$\rm (P)=P_0e^(rt)$ where,

$\rm P_0=initial\;size\n\nr= rate\;of\;growth\n\nt= time \;period$

Now, we put the value in formula we get,

$\rm P_0=10\;grams \n\nwhen ,\n\;\;t=1\;hour P(t)=11 grams\nThen,\n11=10e^{r(1)\n1.1 =e^r\n\n\rm Taking \;log(natural)\;both\;the\; side \;on \;solving\;we\;get,\nln(1.1)=r\;ln(e)\nr=ln(1.1)\nr=0.953101798043\approx0.095$

Now when the bacteria increase its size to triple

$\rm P(t) = 3 * 10 = 30$

Then, according to the formula we substitute values in the formula,

$\rm 30=10e^(0.095t)\n\n3=e^(0.095t)\n\nAgain \;we \;take\;natural\;log\;on \;both\;the\;sides, we\;get\nln\;3=0.095t\n\nt=(\rm ln\;3)/(0.095)\n\n\n\n\rm t= (1.09861228867)/(0.095) \n\n\ t=approx \; 11.56$

Therefore, The bacteria takes 11.56 hours to have tripled in size.

Learn more about logical questions here : brainly.com/question/15046576

Answer 2

Answer:

Answer: It will take 11.56 hours .

Step-by-step explanation:

Exponential growth in population or size formula :

$P(t)=P_0e^(rt)$

, where $P_0$ = initial size

r= rate of growth

t= time period

As per given , we have

$P_0=10$ grams

At t= 1 , P(t)= 11 grams

Then,

$11=10e^(r(1))\n\n 1.1= e^r\n\n\text{Taking natural log on both sides , we get} \n\n\ln (1.1)=r\ln (e)\n\n r=\ln (1.1)\n\n r=0.0953101798043\approx0.095$

When, the bacteria have tripled in size , P(t) = 3 x10 = 30

Then,

$30=10e^(0.095t)\n\n 3=e^(0.095t)$

$\text{Taking natural log on both sides , we get}\n\n \ln 3=0.095t\n\n t=(\ln3)/(0.095)\n\n t=(1.09861228867)/(0.095)\approx11.56$

Hence, it will take 11.56 hours .

Related Questions

The area of a rectangle is at least 115 square centimeters. The width of the rectangle is 5 centimeters and the length of the rectangle is x centimeters. what are the value(s) of x
Solve for x: 4x/5= -20
The United States Bureau of Labor Statistics (BLS) conducts the Quarterly Census of Employment and Wages (QCEW) and reports a variety of information on each county in America. In the third quarter of 2016, the QCEW reported the total taxable earnings, in millions, of all wage earners in all 3222 counties in America. Suppose that James is an economist who collects a simple random sample of the total taxable earnings of workers in 56 American counties during the third quarter of 2016. According to the QCEW, the true population mean and standard deviation of taxable earnings, in millions of dollars, by county are ?=28.29 and ?=33.493, respectively. Let X be the total taxable earnings, in millions, of all wage earners in a county. The mean total taxable earnings of all wage earners in a county across all the counties in James' sample is x??. Use the central limit theorem (CLT) to determine the probability P that the mean taxable wages in James' sample of 56 counties will be less than $33 million. Report your answer to four decimal places. P(x??<33)= Use the CLT again to determine the probability that the mean taxable wages in James' sample of 56 counties will be greater than $30 million. Report your answer to four decimal places. P(x??>30)=
3) g(x) = 4xh(x) = -3x^2 + 4Find (g + h)(x)
Write two ways you could use to find 5 + 8.

How to estimate the quotient of 49.3 divided by 6

Answers

that would be 8 because the answer is 8.21 and you round down to 8

Based on information from the periodic table, what does this image represent? HE 4 Protons e 5 Neutrons = 2 Electrons A. A negatively charged beryllium ion B. A neutral boron atom
C. A neutral beryllium atom
D. A positively charged beryllium ion

Answers

This image represents A positively charged beryllium ion.

We have given that,

He 4 Protons e 5 Neutrons = 2 Electrons

A. A negatively charged beryllium ion

B. A neutral boron atom

C. A neutral beryllium atom

D. A positively charged beryllium ion.

We have to determine, Based on information from the periodic table what does this image represent?

What is the periodic table?

A table of the chemical elements arranged in order of atomic number, usually in rows, so that elements with similar atomic structure (and hence similar chemical properties) appear in vertical columns.

This image represents A positively charged beryllium ion.

To learn more about the periodic table visit:

brainly.com/question/15987580

#SPJ2

Answer:

D. A positively charged beryllium ion

The statement formed when an equal sign is placed between two expressions is called an _______.

Answers

An equation is created when two expressions are separated by an equal sign.

What is an equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

Given, A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is utilized. Based on the degree, there are three different sorts of equations. Equations that are linear, quadratic, and cubic.

Therefore, The statement formed when an equal sign is placed between two expressions is called an equation.

Learn more about the equation here:

brainly.com/question/16255566

#SPJ2

Hello there.

The statement formed when an equal sign is placed between two expressions is called an _______.
equation

Rafael bought a table on sale for $741. This price was 24% less than the original price.What was the original price?