8 million (8 x 106)
can be entered into your
calculator as 8E6
8 and then 2nd function EE
Review of Exponents on
Calculators
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Population Growth Calculations: Exponent Rules and Formula Applications, Exercises of Evolutionary biology
Calculations and formulas for understanding population growth using exponents and the rule of 70. It covers solving for population number (N) and growth rate (k), as well as finding doubling time. Examples include Nigeria, Philippines, Peru, and Liberia.
Typology: Exercises
2021/2022
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8 million (8 x 10 6 ) can be entered into your calculator as 8E
8 and then 2 nd^ function EE
Review of Exponents on Calculators
Calculating population growth N =No e kt
N= Population number (final) No = Original population number e= natural e ( a constant of 2.718… which will be on your scientific calculator) k = growth rate- You must use the decimal form for the formula not the percent If 3.5% growth rate- use 0. If 0.3% growth rate use 0. t= time
Nigeria currently has a growth rate of 2.27% Its population in 2009 was 162 million.
A. If its growth rate stays the same, what will Nigeria’s population be in 2025? B. In 2050?
For this question, you are solving for N so use the formula : N =N (^) o ekt
N (^) o = 162 million (1.62 x 10 8 ) k = 0.0227 (decimal form of 2.27%)
A. t = 16 years N = 1.62 x 10^8 x e(0.0227^ x 16) = 2.33 x 10^8 (233 million people) B. t= 41 years N = 1.62 x 10^8 x e (0.0227^ x 41) = 4.11 x 10^8 (411 million people)
The population of the Philippines was approximately 68 million in 1995. It was approximately 88 million in
- What was the average population growth rate during this time period?
For this question, you are solving for k, so use the formula : k = 1/t ln (N/N (^) o ).
t = 12 years N = 8.8 x 10^7 (88 million) No = 6.8 x 10^7 (68 million)
k = 1/12 ln (8.8/6.8) = 0.0214 or 2.14%
For this question, you are solving for t, so use the formula : t = 1/k ln (N/N (^) o ).
k = 0.0115 (decimal form of 1.15%) N = 4.0 x 10^7 (40 million) No = 2.94 x 10^7 (29,400,000)
t = (1/0.0115) ln (4 / 2.94) = 26.8 years
Rule of 70 Doubling time of a population = 70 / Growth rate (as a percentage)
You will need to memorize this formula for the test. And remember that you use the growth as a percentage in this formula (2.5 if 2.5% growth) as opposed to the decimal form in the growth rate formula.
If you want to see how the rule of 70 is derived, see the Growth Calculations Review Handout (also on my website) which shows how it is derived by solving t = 1/k ln (N/No ) with N/N (^) o = 2.
The doubling time = 70/ 4.
= 15.6 years
Brazil has a population of 200,000,000 and a population growth rate of 1%. If that rate of growth continued, how long would it take for the population to increase in size to 1.6 billion?
In solving this problem determine how many doubling periods this would be.