A particular species of orchid is being studied. The population p p\,p at time t t\,t years after the study started is assumed to be
p=2800ae0.2t1+ae0.2t, where a is a constant. p = \frac{2800ae^{0.2t}}{1 + ae^{0.2t}}, \text{ where } a \text{ is a constant.} p=1+ae0.2t2800ae0.2t, where a is a constant.Given that there were 300 orchids when the study started, show that a=0.12a = 0.12a=0.12.
Use the equation with a=0.12a = 0.12a=0.12 to predict the number of years before the population of orchids reaches 1850.
Show that p=3360.12+e−0.2t\displaystyle p = \frac{336}{0.12 + e^{-0.2t}}p=0.12+e−0.2t336.
Hence show that the population cannot exceed 2800.
7 exam-style questions on Edexcel A Level Old Maths Logs. Each one has a worked solution and a mark scheme showing where the marks go.