Business Calculus Question?

Question

ok ive doing fine on equations but when it came to these word problems...i need help!

The spread of Virus is modeled by the following function w/ respect to t=time=days; V(t)= -t^2+5t-7 where V(t) is the number of people since the first reported viral case was observed. use the "formal definition" of a derivative to find d/dt (V)(t)

thanks guys i appreciate any help!

Answer 1

it could be done by firt principle method
V(t)=t^2+5t-7
V(t+h)=Lt (t+h)^2+5(t+h)-7
h-->0 (h tends to zero)
dV/dt = V(h)=(V(t+h)-V(t)) / h
dV/dt=(h^2+2th+5h ) / h
dV/dt= 2t+5

or by derivating simply

Answer 2

The first poster has correctly computed d/dt. In this instance d/dt represents the rate of change with respect to time.

Answer 3

The "usual" way is:

dV/dt = -2t+5

The limit way is

lim (e->0) {[-(t+e)^2 +5(t+e) -7 - (-t^2) -5t+7]/e}

Now som algebra for teh stuff in the curly brackets:

-t^2-2te-e^2+5t+5e +t^2-5t =-2te+5e

So we get lim(e->0){[-2t+5]e/e} = -2t+5

Answer 4

The derivative of the velocity is the acceleration, I think.
V'(t)=-2t+5