Question

The rate of change of y with respect to t is 3 times the value of the quantity 2 less than y. Find an equation for y, given that y = 212 when t = 0.
You get:

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

Answer 1

\[ \frac{dy}{dt} = 3 \times (y-2) \]\[\int \frac{dy}{y-2} = 3 \int dt\]\[\ln|y-2| = 3t + c\]\[y - 2 = e^{3t+c}\]\[y-2=c_1e^{3t}\]
Using the initial conditions we have:
\[212 - 2 = c_1e^{(0)}\]\[c_1 = 210\]
Substituting back in the equation, we have:
\[y = 210e^{3t} + 2\]
Option C