Video Transcript
A mathematical model predicts that
the population of a city, 𝑥 million, will be given by the formula 𝑥 is equal to
two multiplied by 1.22 to the power 𝑛, where 𝑛 is the number of years from
now. What does the model predict the
population will be in two years’ time?
Let’s begin by considering the
formula we’re given that models the population of a city. It states that 𝑥, the population
in million, is equal to two multiplied by 1.22 to the power of 𝑛, where 𝑛 is the
number of years from now. We are asked to predict the
population in two years’ time.
To do this, we will substitute 𝑛
equals two. 𝑥 is therefore equal to two
multiplied by 1.22 squared. We could type this directly into
the calculator. However, it is worth noting that
1.22 squared is equal to 1.22 multiplied by 1.22. We could work this out by
multiplying 1.22 by one, 0.2, and 0.02 and then finding the sum of these three
answers.
Firstly, 1.22 multiplied by one is
simply 1.22. Multiplying 1.22 by 0.2 gives us
0.244. And multiplying 1.22 by 0.02 gives
us 0.0244. The sum of these three products is
1.4884, and this is the value of 1.22 squared. The population 𝑥 is equal to two
multiplied by this, which is equal to 2.9768. The model predicts that the
population in the city in two years’ time will be 2.9768 million, which could also
be written as 2,976,800.
It is important to note that we
could use this model to predict the population over a longer period of time. For example, if we wanted to
predict the population in 10 years’ time, we could substitute 𝑛 equals 10 into the
formula. This could be repeated for any
number of years moving forwards.
