Answer:
The right answer is :
(a) 23,200
(b) 24,514
(c) 22,926
Step-by-step explanation:
According to the question,
[tex]P_1 = 12000[/tex]
[tex]P_2 = 20000[/tex]
[tex]P_{sat}=80000[/tex]
(a)
We know that the arithmetic growth formula will be:
⇒ [tex]P=Pi+K\times t[/tex]...(1)
here,
⇒ [tex]K=\frac{P_2-P_1}{\Delta t}[/tex]
[tex]=\frac{20000-12000}{25}[/tex]
[tex]=\frac{80000}{25}[/tex]
[tex]=320[/tex]
On putting the values in equation (1), we get
⇒ [tex]P_{2020}=20000+320\times 10[/tex]
[tex]=23,200[/tex]
(b)
The geometric growth formula will be:
⇒ [tex]P=ln(Pi)+K\times t[/tex]
here,
⇒ [tex]K=\frac{lnP_2-lnP_1}{\Delta t}[/tex]
[tex]=\frac{ln(20000)-ln(12000)}{25}[/tex]
By putting the values of general log, we get
hence,
⇒ [tex]P_f=ln(20000)+0.0204\times 10[/tex]
[tex]=10.107[/tex]
[tex]P_{2020}=e^{10.107}[/tex]
[tex]=24,514[/tex]
(c)
⇒ [tex]P_f=P_{sat}-(P_{sat}-P_i)e^{-K\times t}[/tex]
or,
⇒ [tex]K=-\frac{1}{\Delta t}ln(\frac{P_{sat}-P_2}{P_{sat}-P_1} )[/tex]
from here, we get
[tex]=0.005[/tex]
hence,
⇒ [tex]P_{2020}=80000-(80000-20000)e^{-0.005\times 10}[/tex]
[tex]=80000-(60000)e^{-0.005\times 10}[/tex]
[tex]=22,926[/tex]
