Question

Allie found a table of data displaying the number of middle and high school stud enrolled in Lincoln public schools . she made a table with the number of students in the 2015 as year 0 in the table of data.Lookimh at the enrollment in previous years,she decided to use an exponential equation to model the number of students.⚠COULD SOMEONE PLEASE HELP WITH THESE QUESTIONS⚠(Any info will help!!)⛧What is the growth multiplier for the data? complete the table using the multiplier.⛧⛧Write multiplier as a percent.⛧

Answer 1

The general exponential growth formula is:

`y=a\cdot b^x^{}`

where a is the initial amount, b is the growth multiplier, and y and x are the variables.

In this case, x represents years after 2015, y represents the number of students, and the initial value is a = 20,080.

Substituting with y = 20,582 when x = 1, we get:

`\begin{gathered} 20,582=20,080\cdot b^1 \\ (20.582)/(20,080)=b \\ 1.025=b \end{gathered}`

Now, we can complete the table as follows:

`\begin{gathered} x=2 \\ y=20,080\cdot1.025^2=21097 \\ x=3 \\ y=20,080\cdot1.025^3=21624 \\ x=4 \\ y=20,080\cdot1.025^4=22165 \end{gathered}`

Expressing the exponential growth formula with the rate of growth r:

`y=a(1+r)^x^{}`

where b has been replaced by 1 + r. This means that r = 0.025, which expressed as a percent is 0.025*100 = 2.5% growth