b If the number of students five years ago was a, how can you express the number of students three years ago?
C
c How many times do you have to multiply 1500 by the constant multiplier to get the number n years from now?
A
a About 1722 students.
B
b About 1368 students.
C
c f(n) = 1500(1.047)^(n+3)
Practice makes perfect
a A growth rate of 4.7 % means that every year the number of students is 100+4.7=104.7 % of what it was the previous year. This can be written as the following multiplier.
104.7 %=1.047
Notice that this multiplier is constant. Therefore, if the number of students was 1500 three years ago, we can determine the current number of students if we multiply 1500 by 1.047 three times.
1500(1.047)(1.047)(1.047) ≈ 1722
There are currently about 1722 students at the school.
b We want to find the number of students two years prior to the number of students at the school three years ago which was 1500. Let's call this number a. Assuming the annual growth rate was also 4.7 % in the past, we get the following equation.
a(1.047)(1.047)= 1500
Let's solve this equation for a.
Five years ago there were about 1368 students at the school.
c In Part A, we determined that the current number of students could be written as the following numerical expression.
1500(1.047)(1.047)(1.047)
⇕
1500(1.047)^3Each year this number is multiplied by 1.047, so after n years this expression is multiplied by 1.047^n.
f(n) = 1500(1.047)^3* (1.047)^n
Let's simplify this
