To find the inverse, interchange the variables and solve for y.
f^-1 (x) = 4 + x/2
The correct answer is -29.7
Answer:
P(0) = 7,917
Step-by-step explanation:
The population of the community is given by the following formula:
![P(t) = P(0)(1+r)^{t}](https://tex.z-dn.net/?f=P%28t%29%20%3D%20P%280%29%281%2Br%29%5E%7Bt%7D)
In which P(0) is the initial population and r is the growth rate.
The initial population P0 has doubled in 5 years.
This means that
![P(5) = 2P(0)](https://tex.z-dn.net/?f=P%285%29%20%3D%202P%280%29)
Which lets us find r.
![P(t) = P(0)(1+r)^{t}](https://tex.z-dn.net/?f=P%28t%29%20%3D%20P%280%29%281%2Br%29%5E%7Bt%7D)
![2P(0) = P(0)(1+r)^{5}](https://tex.z-dn.net/?f=2P%280%29%20%3D%20P%280%29%281%2Br%29%5E%7B5%7D)
![(1+r)^{5} = 2](https://tex.z-dn.net/?f=%281%2Br%29%5E%7B5%7D%20%3D%202)
Applying the 5th root to both sides
![1+r = 1.1487](https://tex.z-dn.net/?f=1%2Br%20%3D%201.1487)
![r = 0.1487](https://tex.z-dn.net/?f=r%20%3D%200.1487)
So
![P(t) = P(0)(1.1487)^{t}](https://tex.z-dn.net/?f=P%28t%29%20%3D%20P%280%29%281.1487%29%5E%7Bt%7D)
Suppose it is known that the population is 12,000 after 3 years.
With this, we find P(0)
![P(t) = P(0)(1.1487)^{t}](https://tex.z-dn.net/?f=P%28t%29%20%3D%20P%280%29%281.1487%29%5E%7Bt%7D)
![12000 = P(0)(1.1487)^{3}](https://tex.z-dn.net/?f=12000%20%3D%20P%280%29%281.1487%29%5E%7B3%7D)
![1.5157P(0) = 12000](https://tex.z-dn.net/?f=1.5157P%280%29%20%3D%2012000)
![P(0) = \frac{12000}{1.5157}](https://tex.z-dn.net/?f=P%280%29%20%3D%20%5Cfrac%7B12000%7D%7B1.5157%7D)
![P(0) = 7917](https://tex.z-dn.net/?f=P%280%29%20%3D%207917)
16%. You divide those two numbers and then multiply the answer by 100