We want an exponential model of the form y = a(b)x, where y is the number of bacteria after x hours.
- Use the initial condition: at x = 0, y = 5. So a = 5 because y(0) = a·b0 = a.
- Use the 1-hour condition: at x = 1, y = 35. Substitute a = 5 to get 5·b = 35. Solve for b: b = 35/5 = 7.
Therefore the exponential equation is y = 5(7)x.
Interpretation: the population is multiplied by 7 each hour (growth factor 7), so this is rapid exponential growth. The model is valid for x ≥ 0 (hours of sunlight).