Answer:
Step-by-step explanation:
Applying the Laplace transform:
![\mathcal{L}[y'']+5\mathcal{L}[y']+4\mathcal{L}[y']=0](https://tex.z-dn.net/?f=%5Cmathcal%7BL%7D%5By%27%27%5D%2B5%5Cmathcal%7BL%7D%5By%27%5D%2B4%5Cmathcal%7BL%7D%5By%27%5D%3D0)
With the formulas:
![\mathcal{L}[y'']=s^2\mathcal{L}[y]-y(0)s-y'(0)](https://tex.z-dn.net/?f=%5Cmathcal%7BL%7D%5By%27%27%5D%3Ds%5E2%5Cmathcal%7BL%7D%5By%5D-y%280%29s-y%27%280%29)
![\mathcal{L}[y']=s\mathcal{L}[y]-y(0)](https://tex.z-dn.net/?f=%5Cmathcal%7BL%7D%5By%27%5D%3Ds%5Cmathcal%7BL%7D%5By%5D-y%280%29)
![\mathcal{L}[x]=L](https://tex.z-dn.net/?f=%5Cmathcal%7BL%7D%5Bx%5D%3DL)
Solving for 
Apply the inverse Laplace transform with this formula:
![\mathcal{L}^{-1}[\frac1{s-a}]=e^{at}](https://tex.z-dn.net/?f=%5Cmathcal%7BL%7D%5E%7B-1%7D%5B%5Cfrac1%7Bs-a%7D%5D%3De%5E%7Bat%7D)
![y=3\mathcal{L}^{-1}[\frac1{s+4}]=3e^{-4t}](https://tex.z-dn.net/?f=y%3D3%5Cmathcal%7BL%7D%5E%7B-1%7D%5B%5Cfrac1%7Bs%2B4%7D%5D%3D3e%5E%7B-4t%7D)
Answer:
78 mg
Step-by-step explanation:
370 mg - 110 mg = 260 mg (amount decayed in the 8 total years)
260 mg ÷ 8 years = 32.5 mg decayed per year
32.5 × 9 years (years between 2008 and 2017) = 292.5 mg
370 mg - 292.5 mg = 77.5 mg, rounded to 78 mg
Answer negative 9 is the answer
Step-by-step explanation:
Three thousand three hundred and seventy eight
Answer:
y = 5 e^r * t
Let y be the population in billions and t the value of elapsed years
7 = 5 e^r * t is the equation being used where t = 15
7/5 = e^r * t
ln 7/5 = r * t taking ln of both sides
r = .336 / 15 = .0224
y = 5 e^(.0224 t) is then our equation
Check - suppose you want y at 2020
y = 5 e^(.0224 * 20) would be the equation
y = 5 e^.449 = 7.83 billion - seems to be a reasonable answer
