. Based on this model, use a linear approximation to the graph of k(t) at t = 2 to estimate the quantity of the substance at t = 2.1

Question

The quantity of a substance can be modeled by the function k(t) that satisfies the differential equation dk/ dt =-1/90 (k-450). One point on this function is k(2) = 900. Based on this model, use a linear approximation to the graph of k(t) at t = 2 to estimate the quantity of the substance at t = 2.1.

Answer 1

When k=900, dk/dt=-(1/90)(900-450)=-450/90=-5.

Therefore k∽-5t+c. To find c, t=2 when k=900:

900=-10+c, c=910, k=910-5t as an approximate linear equation.

When t=2.1, k=910-10.5=899.5.