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Salma puts $1 000 into the bank. The bank pays 10% interest per year. How long is it before Salma has $1 500 in her account? And in order to plot the graph, we needed points (from some simple calculations) After 1 full year, she has $1000 x 1.1 or $1100 After 2 full years, she has $1000 x (1.1)2 or $1210 After 3 full years, she has $1000 x (1.1)3 or $1331 and so on … Time (in full years) Amount of money ($) 0 1000 1 1100 2 1210 3 1331 4 1464.10 5 1610.51 6 1771.56 The red curve shows the growth of the money in the account We now need to find when the y-coordinate reaches 1500 (hence the blue line) Geogebra will give the coordinates of the point of intersection (point A on the diagram) The answer is – Salma will have $1500 after 4.254 years. The growth of Salma’s money is described by the equation: A = 1000 x (1.1)t And we simply want to solve the equation 1500 = 1000 x (1.1)t This simplifies to 1.5 = (1.1)t Taking logs of both sides … log10 1.5 = log10 1.1t ⇒ log10 1.5 = tlog10 1.1 ⇒ t = log10 1.5 log10 1.1 (using one of our rules of logs) ⇒ t = 4.254 years To some degree the population is growing like Salma’s money Some questions … What’s the starting population? What is the percentage increase per year of the population? http://www.worldometers.info/population/ Or this ….