Edexcel Mathematics Sample paper · Paper 1 · Question 12 · ExamRizz

ExamRizzEdexcel MathematicsMathematics

Sample paper · Paper 1 · Question 12 · 9 marks

12. In a controlled experiment, the number of microbes, N, present in a culture T days after the start of the experiment were counted. N and T are expected to satisfy a relationship of the form N = aTb , where a and b are constants (a) Show that this relationship can be expressed in the form log10N = mlog10T + c giving m and c in terms of the constants a and/or b. (2) log10 T Figure 3 Figure 3 shows the line of best fit for values of log10N plotted against values of log10 T (b) Use the information provided to estimate the number of microbes present in the culture 3 days after the start of the experiment. (4) (c) Explain why the information provided could not reliably be used to estimate the day when the number of microbes in the culture first exceeds 1 000 000. (2) (d) With reference to the model, interpret the value of the constant a.

Lesson: Exponential Functions and Their Graphs