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On November 27, 1993, the New York Times reported that wildlife biologists have found a direct link between the increase in the human population in Florida and the decline of the local black bear population. From 1953 to 1993, the human population increased, on average, at a rate of 8% per year, while the black bear population decreased at a rate of 6% per year. In 1953 the black bear population was 11,000.

(a) The 1993 human population of Florida was 13 million. What was the human population in 1953. (Round to nearest whole person. Do not include commas in answer.)
(b) Find the black bear population in 1993. (Round to nearest whole bear.)
(c) Had this trend continued, in what year would the black bear population have numbered less than 130?

Respuesta :

TomShelby

Answer:

a) 598,402 persons

b) 926 black bears

c) if the trends continues, there will be only 130 bnlack bears by 2025

Explanation:

a) we discount the 1993 population at 8% for  the 40 years period

[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]  

Maturity  13,000,000.00

time  40.00

rate  0.08000

[tex]\frac{13000000}{(1 + 0.08)^{40} } = PV[/tex]  

PV   598,402.1329

b) we calculate considering the rate is negative:

[tex]Principal \: (1+ r)^{time} = Amount[/tex]

Principal 11,000.00

time 40.00

rate           -0.06

[tex]11000 \: (1+ -0.06)^{40} = Amount[/tex]

Amount 925.78 = 926 black bears

c) we need to solve for the time at which:

[tex]11000 \: (1+ -0.06)^{n} = 130[/tex]

[tex](0.94)^{n} = 130/11,000[/tex]

[tex]log_{0.94}(130/11,000) = n[/tex]

n = 71.73

1953 + 72 = 2025

annyksl

The human population in 1953 was 598 people. The population of black bears in 1993 was equal to 926 and if the trend described in the question continued, in 2025 there would be a total of 130 black bears.

We can arrive at this answer as follows:

  • It is possible to calculate the number of people in Florida in 1953 with the following formula:

[tex]\frac{maturity}{(1+rate)^t^i^m^e} = PV\\\frac{13000000}{(1+0.08)^4^0}= PV\\598,402.1329 = PV -------- 598.[/tex]

  • Then we can calculate the population of black bears with the following formula:

[tex]Principal*(1+r)^t^i^m^e = Amount\\11000*(1+(-0.06))^4^0= 925.78 --------- 926[/tex]

  • Lastly, we can calculate what the black bear population will be if the trend continues. This will be done using the following formula:

[tex]Principal *(1+r)^t^i^m^e=Amount\\11000 *(1+0.06)^t^i^m^e= 130\\(0.64)^t^i^m^e=130/11000\\log_0_._9_4(130/11000)=time\\time= 71.73 ---- 72\\[/tex]

  • Finally, we must consider that:

[tex]1953+72= 2025[/tex]

Thus, we can consider that in 2025 the number of black bears will be equal to 130.

More information:

https://brainly.com/question/3096776?referrer=searchResults

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