Initially 1600 cells. After 2 hours increased to 1700 cells. Assume it is an exponential function of time. Instantaneous growth rate be 200 cells per hour?

Question

Don't really know how to relate the terms into an equation. 

Answer 1

Exponential growth is modeled by the equation y = pe^rt , where p is the initial or principal amount, e is Euler's number, r is the exponential growth rate, t is the amount of time, and y is the total amount after that time.  We are given that p = 1600.

 

At two hours, t = 2, y = 1700, and plugging the values in, 1700 = 1600 e^{(r * 2)}. We can solve for r = ln(1700/1600) / 2 ≈ 0.0303.

 

The instantaneous growth rate of cells is dy/dt.  If y = 1600e^0.0303t, then dy/dt = 1600e^0.0303t * 0.0303 = 48.48e^0.0303t.

 

Then you can solve for the time t when dy/dt = 200.