he rate of change of y with respect to t is 3 times the value of the quantity 2

Question

less than y. Find an equation for y, given that y = 212 when t = 0.
You get:

A. y = 212e^3t - 2
B. y = 210e^3t +2
C. y = 212e^3t +2
D. y= 214e^3t - 2
E. y = 210e^3t - 2

Answer 1

ever think of typing real math?
dy/dt = 3(y-2)
dy/(y-2) = 3dt
ln(y-2) = 3t+c
y-2 = c*e^(3t)
Since y(0) = 212, c = 210
y = 210e^(3t)+2

Answer 2

Thank you it was correct :)

Answer 3

Can you help me with this one, please

The rate of change of y with respect to x is one-half times the value of y. Find an equation for y, given that y = -7 when x = 0.
You get:
A. y=-7e^0.5x
B. y=e^0.5x -7
C. y=-7(1/2)^x
D. y=-7(1/2)e^x
E. dy/dx=1/2*y

Answer 4

dy/dx = y/2
dy/y = (1/2) dx
ln y = x/2 + C
y = c e^(x/2)
y = -7 e^(x/2) which is A

Answer 5

It really so say he