Question

The function f(x)=830(1.2)^× represents the number of students enrolled at a university x years after it was founded. Each year,the number of students is _ the number the year before.A. 2 timesB. 1.2 timesC. 2 more thanD. 0.2 times

Answer 1

Solving Exponential Functions.

`\begin{gathered} f(x)=830(1.2)^x \\ \text{Step 1: Take 2 consecutive numbers for the values of x.} \\ \text{Let x=2 and x=3} \\ \text{Substituting these values for x respectively, we get,} \\ \text{When x=2,} \\ f(2)=830(1.2)^2=1195.2 \\ \text{When x=3,} \\ f(3)=830(1.2)^3=1434.24 \\ \text{Rate of increase in the number of students enrolled in the university each year is} \\ (1434.24)/(1195.2)=1.2 \end{gathered}`

The correct answer is 1.2 times (option B)