







Exponential growth 
20160126 

From Paul: The value of a stamp was 0.03 in 1851. The value in 2011 is $50,000. If the value increased exponentially, what is the annual growth rate? Answered by Penny Nom. 





How fast did Jessica grow? 
20140410 

From jasmine: when she was 14 jessica was 5 feet, 4inches tall . at 18 she is now 6 feet, 2inches tall .how fast did jessica grow during this time Answered by Robert Dawson. 





The growth of a tree 
20140216 

From Emily: If a tree is 10 ft tall after 2 years and 25 ft tall after 5 yrs , find the rate of change of growth
Of the tree if y is the height in ft and x is the number of years. Answered by Penny Nom. 





Percentage increase 
20120801 

From Jay: When calculating percentage growth, why is (yx)/x the same as
(y/x)1 ??? (I seem to be stuck on the simple algebra here)...
e.g. 2011, toy was £5, 2012, toy is £10. What is the percentage
increase? So, (105)/5 = 1 (i.e. 100% increase), AND, (10/5)1 = 1
(i.e. also 100% increase).
Thanks in advance. Answered by Penny Nom. 





An exponential equation 
20101019 

From Sandi:
Question from sandi, a student:
I have several questions similar to this one and was wondering if you could walk me through this one. I'm totally lost on how to do it.
Paramecia reproduce by splitting in two. In a laboratory flask, a colony of paramecia had an initial population of 500. Each day, the population of the paramecia was counted. The results are as listed.
Time (in days)Population
0500
1600
2720
3864
41037
51244
61493
71792
82150
1.)Using graphing calculator make a scatter plot of the data in table.
I think I did this part right I set my window at Xmin=0 Xmax=10 Xscl=1 Ymin=0 Ymax=2500 Yscl=100 Xres=1
2.) Determine an exponential equation to represent the population as a function of time without using a graphing calculator.I have no clue how to do this.
3.)Suppose the flask and food supply is large enough to support the trend of the population growth. Estimate the population of the colony when the time is 10 days. Answered by Penny Nom. 





Linear growth 
20100127 

From S.: I. Linear Growth:
Suppose that the town has a fixed increase in population growth number of population increase each year.
Choose the amount of population growth each year = 200
(Hint: Choose a whole number for your growth rate, rather than a percent.)
a) Fill in the following chart:
Year (t) Population (P)
t = 0
(2010) 1000
t = 1
(2011) 1000+200=1200
t = 2
(2012) 1000+400=1400
t = 3
(2013) 1000+600=1600
b) Find a linear equation in the form P = mt + b (y = mx + b), which gives the population, P, t years from 2010.
. . .
Answered by Melanie Tyrer. 





Growth rates 
20100126 

From Bhavya: Dear Sir/Ma'am,
I read in the text book that the growth rates of these 3 functions are as below
n^{2/3} < n/lg n < n^{0.99}
I tried the substitution method to check the correctness of this. But it gets really tough as n increase.
Is there any simpler way to understand the correctness of these growth rates?
Thanks and Regards,
Bhavya Answered by Robert Dawson. 





Annual percent growth 
20081213 

From Joe: If WallMart had sales of $58,200,000,000 in the year 2002 and $90,800,000,000 in the year 2006.
1. Find what percent that increase is of the 2002 sales? I came up with (9.08*10^10  5.82*10^10) / 5.82*10^10 * 100 = 56.01% increase. Is this correct?
2. What was the percent GROWTH in WalMart's sales from 20022006? I am having trouble figuring out how to do the Growth problem. I would appreciate any help. Answered by Harley Weston. 





A linear model 
20080509 

From Shelby: How would you write a linear model to represent the population of a city that has a population of 547,725 and a growth rate of 25,195 per year with t represents the number of years since 1994? Answered by Penny Nom. 





Growth factor and growth rate 
20080213 

From william: what is the difference between growth factor and growth rate? Answered by Stephen La Rocque and Harley Weston. 





Exponential Growth 
20071119 

From lisa: Hi i am a 8th grader who is learning about algebra
and we are having test on exponent and i don't really get it
i asked my teacher and she told me i should pay more attention
so i want to know what exponential Growth means Answered by Penny Nom. 





Linear growth 
20070511 

From Rebecca: What is the definition of linear growth? Answered by Penny Nom. 





Exponential decay 
20060329 

From Casey: Fifty milligrams of a drug was injected into a patient at 6am. The drug is known to be eliminated according to the law of exponential decay. At 8.30am it was determined that 60% of the drug remained in the body. How many milligrams will remain in the body at midday? Answered by Penny Nom. 





Aunt Lucy's letter 
20040627 

From Olivia: "Dear bob,
now that i am getting on (70 today). i want to give you some of my money, i shall give you a sum each year, starting now. you can choose which of the following schemes you would like me to use.
a) £100 now, £90 next year,£80 the yaer after and so on.
b) £10 now, £20 next year, £ 30 the next year and so on.
c) £10 now, 1.5 times as much next year, 1.5 times as much the year after that and so on.
d)£1 now, £2 next year, £ 4 the year after, £8 the year after and so on.
of course these schemes will only operate while i am alive. i look forward to hearing which scheme you choose and why!
Best wishes,
Aunt Lucy." Answered by Penny Nom and Claude Tardif. 





Conservation, consumption and population growth 
20010604 

From Steve: I'm trying to quantify the relation between conservation/consumption and population growth. For instance let's consider California: The 2000 census states that California's population grew from 29,760* in 41990 to 33,871 in 42000. I want to find r or rate of growth per year. Based on the exponential growth formula for population growth: . . . Answered by Penny Nom. 





Population growth 
20010501 

From Gina: Suppose the population of a country increases at a steady rate of 3% a year. If the population is 50 million at a certain time, what will it be 25 years later? Define the recurrence relation that solves this problem. Answered by Penny Nom. 





A colony of bacteria 
20000422 

From Nicci Demmin: Suppose that the bacteria in a colony can grow unchecked, by the law of exponential change. The colony starts with one bacterium and doubles every half hour. How many bacteria will the colony contain at the end of 50 hours? Answered by Penny Nom. 

