2. Exponential decay: The African Elephant Database project estimates that there were 225,200 African elephants (Lavadente Africana) in Central Africa in 1995. The estimate for the same region in 1998 was 125,500 elephants. For this project, Central Africa consisted of the countries of Cameroon, Central African Republic, Chad, Congo, Democratic Republic of Congo, Equatorial Guinea, and Gabon. [15 pts totall Assume that the elephant population was decreasing by the same rate each year. Calculate the yearly decay multiplier (1-r) for Central African elephants (report 4 significant figures), then write an exponential function modeling the elephant population using y for the population and t for the-time yea(1-r) Pop 1495 225,200 = a Pop 1998 125, 500= y +1998-1995-3 125,500 = 22,200 (1-1) y-225900 (6.8229) 225, 2,00 125500 221200 225,200 (1-+) 125500√(1-1) 225200 0.8229 Problem Set 2 ENVS 25 | Spring 2024 (1-1)- 0.8229 Exponential function: y-225.200/a 8229) b. Without calculations (just looking at the data provided), estimate the half-life for this elephant population. Now calculate the half-life for this population using your answer to part a, reporting in the box below with 3 significant figures. How does your calculation compare with your rough estimate Gust a gut check, you do not need to provide a written answer)?.. 9½ = 2 =0.3. 223200 = 22200 (0.8229)+v 0.5= (0.8229) In0.5 In (0.82) Ino.sty In 0.8229 Ino.8zza Ino.8229 tz = 3.56 years Calculated half-life: 3.56 years Problem Set 2 ENVS 25 | Spring 2024 c. Suppose that the critical value of the Central African elephant population is 1,000 individuals; if the population falls below this level, the Central African elephants will go extinct. Assuming the same decay rate, when (in which year) will or was this population level reached? (round to nearest year); Year:
2. Exponential decay: The African Elephant Database project estimates that there were 225,200 African elephants (Lavadente Africana) in Central Africa in 1995. The estimate for the same region in 1998 was 125,500 elephants. For this project, Central Africa consisted of the countries of Cameroon, Central African Republic, Chad, Congo, Democratic Republic of Congo, Equatorial Guinea, and Gabon. [15 pts totall Assume that the elephant population was decreasing by the same rate each year. Calculate the yearly decay multiplier (1-r) for Central African elephants (report 4 significant figures), then write an exponential function modeling the elephant population using y for the population and t for the-time yea(1-r) Pop 1495 225,200 = a Pop 1998 125, 500= y +1998-1995-3 125,500 = 22,200 (1-1) y-225900 (6.8229) 225, 2,00 125500 221200 225,200 (1-+) 125500√(1-1) 225200 0.8229 Problem Set 2 ENVS 25 | Spring 2024 (1-1)- 0.8229 Exponential function: y-225.200/a 8229) b. Without calculations (just looking at the data provided), estimate the half-life for this elephant population. Now calculate the half-life for this population using your answer to part a, reporting in the box below with 3 significant figures. How does your calculation compare with your rough estimate Gust a gut check, you do not need to provide a written answer)?.. 9½ = 2 =0.3. 223200 = 22200 (0.8229)+v 0.5= (0.8229) In0.5 In (0.82) Ino.sty In 0.8229 Ino.8zza Ino.8229 tz = 3.56 years Calculated half-life: 3.56 years Problem Set 2 ENVS 25 | Spring 2024 c. Suppose that the critical value of the Central African elephant population is 1,000 individuals; if the population falls below this level, the Central African elephants will go extinct. Assuming the same decay rate, when (in which year) will or was this population level reached? (round to nearest year); Year:
Chapter12: Sequences, Series And Binomial Theorem
Section12.3: Geometric Sequences And Series
Problem 12.58TI: What is the total effect on the economy of a government tax rebate of $500 to each household in...
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Using the information and answers above, solve for question c.
Transcribed Image Text:2. Exponential decay: The African Elephant Database project estimates that there were 225,200 African
elephants (Lavadente Africana) in Central Africa in 1995. The estimate for the same region in 1998 was 125,500
elephants. For this project, Central Africa consisted of the countries of Cameroon, Central African Republic,
Chad, Congo, Democratic Republic of Congo, Equatorial Guinea, and Gabon. [15 pts totall
Assume that the elephant population was decreasing by the same rate each year. Calculate the yearly decay
multiplier (1-r) for Central African elephants (report 4 significant figures), then write an exponential
function modeling the elephant population using y for the population and t for the-time
yea(1-r)
Pop 1495 225,200 = a
Pop 1998 125, 500= y
+1998-1995-3
125,500 = 22,200 (1-1) y-225900 (6.8229)
225, 2,00
125500
221200
225,200
(1-+)
125500√(1-1)
225200
0.8229
Problem Set 2
ENVS 25 | Spring 2024
(1-1)-
0.8229
Exponential function:
y-225.200/a 8229)
b. Without calculations (just looking at the data provided), estimate the half-life for this elephant population.
Now calculate the half-life for this population using your answer to part a, reporting in the box below with
3 significant figures. How does your calculation compare with your rough estimate Gust a gut check, you do
not need to provide a written answer)?..
9½
=
2
=0.3. 223200 = 22200 (0.8229)+v
0.5= (0.8229)
In0.5 In (0.82)
Ino.sty In 0.8229
Ino.8zza
Ino.8229
tz
= 3.56 years
Calculated half-life:
3.56
years
Problem Set 2
ENVS 25 | Spring 2024
c. Suppose that the critical value of the Central African elephant population is 1,000 individuals; if the
population falls below this level, the Central African elephants will go extinct. Assuming the same decay
rate, when (in which year) will or was this population level reached? (round to nearest year);
Year:
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