Answer:
a. 1 263 888
b. 130 701
c. 72 years
Step-by-step explanation:
a. The differential equation applies here.
Let the quantity increase for a certain time be given by Q(t)
Every unity of time, the quantity increases by [tex]1+\frac{r}{100}[/tex] so that after the time t, the quantity remaining will be given by:
[tex]Q(t) = (1+ \frac{r}{100} )^{t}[/tex]
In a similar manner, the quantity R(t) decreases at a rate given by the following expression:
[tex]1-\frac{r}{100}[/tex] and after the time , t the quantity of R remaining will be given by:
[tex]R(t) = (1-\frac{r}{100} )^{t}[/tex]
a. To find the population of humans in 1953
[tex]Q(t) = (1+ \frac{r}{100} )^{t}[/tex]
1993 - 1953 = 40 years = t
Q(40) = Q×[tex]1.06^{40}[/tex]
Q = 1 263 888.44
≈ 1 263 888
b. For bear population in 1993:
[tex]R(t) = (1-\frac{r}{100} )^{t}[/tex]
t = 40
R(40) = [tex]b 0.94^{40} = 11 000[/tex]
b = 130 700. 889
≈130 701
c. time taken for black bear population number less than 100 is given by:
130 = 11000×[tex]0.94^{t}[/tex]
solving using natural logarithms gives t = 72.72666
= 72 years Ans
