# Exponential Models in the Sciences

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## Objective

SWBAT Model scientific phenomena with exponential functions in order to solve problems.

#### Big Idea

Continuous growth is an important concept in biology, physics and chemistry. Exponential models can be used to describe continuous change and predict unknown quantities.

## Modeling Activity

40 minutes

To help my students understand the power of a mathematical model, I present them with a bivariate data set that can be modeled with an exponential function.  NSpire Exponential Regression Cooling Coffee.docx is an activity that walks students through the steps of performing an exponential regression on cooling data [MP4].

I ask students to complete this activity independently so that every student gets practice manipulating the graphing calculator.  As students work on this activity, I circulate to provide help with the technology as needed [MP6].

## Workshop: Exponential Models in the Sciences

60 minutes

The exponential function unit provides many opportunities to connect what students are doing in math class to topics they study in other high school classes.  Through conversations with science, social studies, and business teachers at my school I have developed several problem sets that help my students see these connections.  WS Exponential Problems in Science.docx is a problem set that focuses on exponential content from biology, chemistry and physics.

I provide each student with a copy of WS Exponential Problems in Science and make the answer key available through Edmodo.  Students spend the remainder of the class working through this packet with my help and the help of their peers.

## Exit Ticket

15 minutes

My students have spent the period delving into some challenging exponential word problems which they will complete for homework.  It is likely that only a few of my students will completely understand every problem in the set.  However, it is essential that every student can apply continuous growth models  of the form N(t)=Noe^(kt) [MP4].  Exit Ticket Radioactive Decay is a half sheet that I ask each student to complete and turn in to me before they leave class.  Evaluating these exit tickets helps me know whether to spend more time in whole-class discussions about these problems, or whether to pull individual students aside for more instruction.