Answer:
z=12
Step-by-step explanation:
6*2=12
z=12
Answer:
![P(t) = P(0)e^{0.0693t}](https://tex.z-dn.net/?f=P%28t%29%20%3D%20P%280%29e%5E%7B0.0693t%7D)
Step-by-step explanation:
The population of a community is known to increase at a rate proportional to the number of people present at time t.
This means that the population growth is modeled by the following differential equation:
![\frac{dP(t)}{dt} = rP(t)](https://tex.z-dn.net/?f=%5Cfrac%7BdP%28t%29%7D%7Bdt%7D%20%3D%20rP%28t%29)
Which has the following solution:
![P(t) = P(0)e^{rt}](https://tex.z-dn.net/?f=P%28t%29%20%3D%20P%280%29e%5E%7Brt%7D)
In which P(t) is the population after t years, P(0) is the initial population and r is the growth rate.
The population has doubled in 10 years
This means that
. We use this to find r.
![P(t) = P(0)e^{rt}](https://tex.z-dn.net/?f=P%28t%29%20%3D%20P%280%29e%5E%7Brt%7D)
![2P(0) = P(0)e^{10r}](https://tex.z-dn.net/?f=2P%280%29%20%3D%20P%280%29e%5E%7B10r%7D)
![e^{10r} = 2](https://tex.z-dn.net/?f=e%5E%7B10r%7D%20%3D%202)
![\ln{e^{10r}} = \ln{2}](https://tex.z-dn.net/?f=%5Cln%7Be%5E%7B10r%7D%7D%20%3D%20%5Cln%7B2%7D)
![10r = \ln{2}](https://tex.z-dn.net/?f=10r%20%3D%20%5Cln%7B2%7D)
![r = \frac{\ln{2}}{10}](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7B%5Cln%7B2%7D%7D%7B10%7D)
![r = 0.0693](https://tex.z-dn.net/?f=r%20%3D%200.0693)
So the equation that will estimate the population of the community in t years is:
![P(t) = P(0)e^{0.0693t}](https://tex.z-dn.net/?f=P%28t%29%20%3D%20P%280%29e%5E%7B0.0693t%7D)
ANSWER
For Jamal statement to be true,
![c = \frac{b}{a}](https://tex.z-dn.net/?f=c%20%3D%20%5Cfrac%7Bb%7D%7Ba%7D%20%20)
EXPLANATION
The given statement is:
ax + b = a(x + c)
We expand the left hand side to obtain,
ax + b = ax + ac
Subtract ax from from both sides of the equation.
b=ac
We know that, a≠0 , so we can divide through by 'a'.
![\frac{b}{a} = c](https://tex.z-dn.net/?f=%20%5Cfrac%7Bb%7D%7Ba%7D%20%20%3D%20c)
Answer:
There were 16 birds at the shelter on Wednesday.
Step-by-step explanation:
Number of cats and birds on Wednesday = 34
let the number of birds on Wednesday = b
Then number of cats = (34 -b)
The rate of taking care of each bird in shelter = $3
The rate of taking care of each cat in shelter = $7
Total amount spent by shelter on Wednesday = $174
So, according to the question
b x ($3) + (34 -b) ($7) = $ 174
or, 3b + 238 - 7b = 174
or, 4b = 64
⇒ b = 64/4 = 16
Hence, the number of birds in shelter on Wednesday = b = 16
and Number of cats = 34 - 16 = 18