Question

1. What is the difference between an exponential growth and exponential decay? 2. What is an example equation for expoential growth and an example equation for exponential decay?

Answer 1

Answer: see below

Explanation:

The standard form of an exponential equation is: y = a(b)ˣ where

• a is the initial value
• b is the rate

Growth:

Exponential growth is where the final value (y) is greater than the initial value (a).

An example would be the spreading of a rumor:

You tell 1 person (a = 1) who then tells 2 people each minute (b = 2). How many people will they have spread the rumor to after 5 minutes (x = 5)?

y = 1(2)⁵

= 32

Decay:

Exponential decay is where the final value (y) is less than the initial value (a).

An example would be the decrease of bacteria in a person:

A person has 100 bacteria (a = 1) who takes a pill that is supposed to cut in half the number of bacteria each hour (b = 1/2). How many bacteria will the person have after 2 hours (x = 2)?

`y=100\bigg((1)/(2)\bigg)^2\\\\\\.\quad =100\bigg((1)/(4)\bigg)\\\\\\.\quad = 25`