APFIVE Differential Equation for Exponential Growth
A population is observed to grow in a manner consistent with exponential growth. Without using a calculator and using the data provided in the table, determine which differential equation best represents the growth of the population $$P(t)$$.
| Time (years) | Population |
|---|---|
| 0 | 100 |
| 1 | 120 |
| 2 | 144 |
A
$$\frac{dP}{dt} = k+P$$
B
$$\frac{dP}{dt} = k*P$$
C
$$\frac{dP}{dt} = \frac{P}{k}$$
D
$$\frac{dP}{dt} = k*P^2$$
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