Mathematical+Reflections,+p+30

Ab.S 15th september Main Idea: Essential Question: Notes: No notes taken since the document is a Mathematical Reflections.

1.
 * Mathematical Reflections**
 * Question: Suppose you had data about the growth of a fish population in a lake over several years.**

a. **How would you decide whether the population was growing exponentially?**

You would decide whether the population was growing exponentially by looking to see if the population multiplies or divides by the same number each time and you if it has a growth or a decay factor. You can also look to see if the graph model starts out pretty low but rises rapidly until it is almost a straight line.

b**. Question: If the population growth appeared to be exponential, how would you use the data to write an equation for the growth?**

You would use your data to write an equation for the growth by letting the starting population be the “a” for the equation or the y-intercept and let the growth factor number be the slope for the equation and let the slope be multiplied by x which is going to be your exponent.

2. **Question: How is a growth rate of 20% related to an exponential growth factor of 1.2?**

It is related to the growth rate of 20% by because 20% of any number added to that number will be the same as saying that initial number multiplied by 1.2.

3. **Suppose rents in a particular area are increasing by 20% per year.**

a. **Predict what an apartment that now rents for $1500 per month will rent for each year for the next 5 years. Explain your work.**

It will rent $1800 for 1 year from now because 20% of $1500 is $300, so $1500 + $300 is $1800.

b. **Predict what an apartment that now rents for $1500 per month will rent for each year for the next 5 years. Explain your work.**

The apartment will rent $1800 for the first year, $2,160 for the second year, $2,592 for the third year, $3,110.40 for the fourth year and $3,732.48 for the fifth year because if you keep on multiplying 1500 for 5 years with 20%growth, it will end up being $3,110.40 for the fifth year.

c. The equation would be R=$1500(1.2ˆt) because the starting rent is $1500 and the rent grows 20% each time which is the same as saying that it multiplies by 1.2 each time, so that will be your slope which will be multiplied to exponent of x.


 * Summary: In this investigation, we learned about compound growth. Compound growth is used for doing problem that deal with interest, the monetary unit or a yearly growth. We also learned how the initial value affects the yearly growth and how it affects the growth factor. We also learned how to make tables, make graphs and write equations for such relationships.**