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Common Core (Functions)

Common Core for Mathematics

Examples, solutions and lessons to help High School students learn how to write a function that describes a relationship between two quantities.

A. Determine an explicit expression, a recursive process, or steps for calculation from a context.

- Given a linear, exponential, or quadratic context, find an explicit algebraic expression or series of steps to model the context with mathematical representations

Common Core: HSF-BF.A.1

The following diagram shows the recursive formula and explicit formula for exponential growth. Scroll down the page for more examples and solutions on exponential growth.

**Recursive and Explicit Equations**

Common Core State Standard F-BF.1. Explanation of Recursive equations and Explicit Equations.

Recursive functions are functions that repeat a process on successive values to generate the next value. The next number in a sequence is found by performing the operation on the current number in the sequence.

Example:

Give the recursive and the explicit equation to represent the situation.

Bobby shares a Youtube video with three of his friends on Facebook. Within 1 minute each of those friends share the video with three of their friends. How many people received the video during the 10th minute?

**Exponential Growth: Recursive and Explicit Equations Part 1**

This video explains how to express exponential growth using recursive and explicit equations.

Example:

There are 4,000 students attending a local community college and the number of students is increasing by 5% each year. How many students will attend the college in 4 years?

**Exponential Growth: Recursive and Explicit Equations Part 2**

This video explains how to express exponential growth in recursive form and in explicit form.

Example:

An ant colony is growing according to an exponential growth model with P0 = 80 and P1 = 92 where n is the of days.

- Find the recursive formula for the growth.
- Find the explicit formula for the growth.
- Determine the population after 30 days.
- Graphically determine when the population will reach 990.

**Ex: Find an Recursive and Explicit Equation for Exponential Growth**

Given Two Function Values

This video provides an example of how to find a recursive and explicit equation for exponential growth given two function values.

Example:

A population growth according to an exponential growth model P0 = 10 and P_{1} = 98.

Find the recursive formula.

Find the explicit formula.

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