TMA 02Cut-off date20 January 2021Question 1– 5 marks
You should be able to answer this question after studying Unit 3.Use a table of signs to solve the in equalityy−32y+ 7≥0.Give your answer in interval notation.
[5]Question 2– 5 marksYou should be able to answer this question after studying Unit 3.The population growth of bacteria can in some circumstances be modelled by an exponential growth function. This growth can be measured bychecking the bacterial density (the number of bacteria in a given volume).
This is done by finding how much light the bacteria in a test tube willabsorb, measured in absorbance units (AU).Suppose thatf(t) is the density of bacteria in a particular sample at timet(in hours). Assume that the density of bacteria, in AU, is modelled by theexponential growth functionf(t) =Bekt(t≥0),whereBandkare constants.
After 2 hours the density was 0.0436 AU, andafter 6 hours the density was 0.0978 AU.(a) Show that the value of the constantkis 0.202 to three significant figuresand find the value of the constantB, correct to three significant figures.
[4](b) What is the bacterial density, in AU, predicted by the model after9 hours? Give your answer to three significant figures
.[1]Hint: make sure you use accurate values ofBandk, if you found thesein part
(a). You may use rounded values if you do not have accuratevalues but you will lose marks for this.