Differential Equation for Exponential Growth
The table shows data for a population, $$P(t)$$, that is growing exponentially. Which of the following differential equations could model the growth of this population?
| Time (years) | Population |
|---|---|
| 0 | 100 |
| 1 | 120 |
| 2 | 144 |
A
$$\frac{dP}{dt} = \frac{P}{k}$$
B
$$\frac{dP}{dt} = k+P$$
C
$$\frac{dP}{dt} = k*P^2$$
D
$$\frac{dP}{dt} = k*P$$
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