Answer:
![\frac{\ln 4}{k}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cln%204%7D%7Bk%7D)
Step-by-step explanation:
Given equation that shows the change in population with respect to time,
![\frac{dP}{dt}=kP](https://tex.z-dn.net/?f=%5Cfrac%7BdP%7D%7Bdt%7D%3DkP)
![\frac{dP}{P}=kdt](https://tex.z-dn.net/?f=%5Cfrac%7BdP%7D%7BP%7D%3Dkdt)
On integrating,
![\ln P = kt + C](https://tex.z-dn.net/?f=%5Cln%20P%20%3D%20kt%20%2B%20C)
![\implies P = e^{kt+C}](https://tex.z-dn.net/?f=%5Cimplies%20P%20%3D%20e%5E%7Bkt%2BC%7D)
![P=e^C e^{kt}](https://tex.z-dn.net/?f=P%3De%5EC%20e%5E%7Bkt%7D)
Put ![e^C=P_0](https://tex.z-dn.net/?f=e%5EC%3DP_0)
![P = P_0 e^{kt}](https://tex.z-dn.net/?f=P%20%3D%20P_0%20e%5E%7Bkt%7D)
According to the question,
If P = A if t = 0,
![A = P_0 e^0\implies A = P_0](https://tex.z-dn.net/?f=A%20%3D%20P_0%20e%5E0%5Cimplies%20A%20%3D%20P_0)
Thus, the required function,
![P = A e^{kt}](https://tex.z-dn.net/?f=P%20%3D%20A%20e%5E%7Bkt%7D)
If the final population = 4A,
![4A = A e^{kt}](https://tex.z-dn.net/?f=4A%20%3D%20A%20e%5E%7Bkt%7D)
![4 = e^{kt}](https://tex.z-dn.net/?f=4%20%3D%20e%5E%7Bkt%7D)
Taking natural log both sides,
![\ln 4 = \ln e^{kt}](https://tex.z-dn.net/?f=%5Cln%204%20%3D%20%5Cln%20e%5E%7Bkt%7D)
![\ln 4 = kt\ln e](https://tex.z-dn.net/?f=%5Cln%204%20%3D%20kt%5Cln%20e)
![\ln 4 = kt](https://tex.z-dn.net/?f=%5Cln%204%20%3D%20kt)
![\implies t = \frac{\ln 4}{k}](https://tex.z-dn.net/?f=%5Cimplies%20t%20%3D%20%5Cfrac%7B%5Cln%204%7D%7Bk%7D)
Hence, after
time, the population will be quadruple its initial value.
Answer:
y = 2x+4
Step-by-step explanation:
slope (m) = 2
point (-1,2)
so,
b = 2-2×(-1) = 4
y = mx+b
or, y = 2x+4
Answer:
119×7.5 =892.5
you need 119 stitches that are each 7.5 inches so you would use that equation to get your answer