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 ….