Answer:
y (t) = 19 + 76*e^(-(1/51)*t)
Step-by-step explanation:
We have the following differential equation model:
dy / dt = - (1/51) * (y -19)
The initial conditions are: y (0) = 95 and y '(70) = 1
We solve the differential equation, separating variables:
1 / (and -19) * dy = - (1/51) * dt
we integrate on both sides:
ln (y -19) = - (1/51) * t + C
e ^ ln (y -19) = e ^ (- (1/51) * t + C)
y - 19 = C1 * e ^ (- (1/51) * t)
y = 19 + C1 * e ^ (- (1/51) * t)
replacing, and (0) = 95
95 = 19 + C1 * e ^ (- (1/51) * 0)
95 = 19 + C1 * e ^ 0
95 = 19 + C1
C1 = 95 - 19 = 76
Therefore the equation would be:
y (t) = 19 + 76 * e ^ (- (1/51) * t)
