A quantity varies exponentially with time (in hours)
MATHEMATICS · Multi-part · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions
Problem
A quantity Q varies exponentially with time x (in hours). At x=0 the quantity is 4 units, and at x=2 hours it is 16 units.
(i) Show that an equation of the form Q(x)=abx satisfies the given information and determine the values of a and b.
(ii) Using the equation obtained, calculate Q(−1).
(iii) State the coordinates of the y-intercept and write the equation of the horizontal asymptote.
(iv) Classify the behaviour of the curve as exponential growth or exponential decay, giving a brief reason.
(v) Draw a neat sketch of the graph, labelling the intercept, the point (2,16) and the horizontal asymptote.