In this section, we are going to see how to solve word problems on exponential growth and decay.

Before look at the problems, if you like to learn about exponential growth and decay,

**Problem 1 :**

David owns a chain of fast food restaurants that operated 200 stores in 1999. If the rate of increase is 8% annually, how many stores does the restaurant operate in 2007 ?

**Solution :**

Number of years between 1999 and 2007 is

n = 2007 - 1999

n = 8

No. of stores in the year 2007 = **P(1+r)ⁿ**

Substitute P = 200, r = 8% or 0.08 and n = 8.

No. of stores in the year 2007 = 200(1 + 0.08)^{8}

No. of stores in the year 2007 = 200(1.08)^{8}

No. of stores in the year 2007 = 200(1.8509)

No. of stores in the year 2007 = 370.18

So, the number of stores in the year 2007 is about 370.

**Problem 2 :**

You invest $2500 in bank which pays 10% interest per year compounded continuously. What will be the value of the investment after 10 years ?

**Solution :**

We have to use the formula given below to know the value of the investment after 3 years.

**A = Pe ^{rt}**

Substitute

P = 2500

r = 10% or 0.1

t = 10

e = 2.71828

Then, we have

A = 2500(2.71828)^{(0.1)10}

A = 6795.70

So, the value of the investment after 10 years is $6795.70.

**Problem 3 :**

Suppose a radio active substance decays at a rate of 3.5% per hour. What percent of substance will be left after 6 hours ?

**Solution :**

Since the initial amount of substance is not given and the problem is based on percentage, we have to assume that the initial amount of substance is 100.

We have to use the formula given below to find the percent of substance after 6 hours.

**A = P(1 + r) ^{n}**

Substitute

P = 100

r = -3.5% or -0.035

t = 6

(Here, the value of "r" is taken in negative sign. because the substance decays)

A = 100(1-0.035)^{6}

A = 100(0.935)^{6}

A = 100(0.8075)

A = 80.75

Because the initial amount of substance is assumed as 100, the percent of substance left after 6 hours is 80.75%

**Problem 4 :**

The number of bacteria in a certain culture doubles every hour. If there were 30 bacteria present in the culture initially, how many bacteria will be present at the end of 8th hour?

**Solution :**

Note that the number of bacteria present in the culture doubles at the end of successive hours.

Since it grows at the constant ratio "2", the growth is based is on geometric progression.

We have to use the formula given below to find the no. of bacteria present at the end of 8th hour.

**A = ab ^{x}**

Substitute

a = 30

b = 2

x = 8

Then, we have

A = 30(2^{8})

A = 30(256)

A = 7680

So, the number of bacteria at the end of 8th hour is 7680.

**Problem 5 :**

A sum of money placed at compound interest doubles itself in 3 years. If interest is being compounded annually, in how many years will it amount to four times itself ?

**Solution :**

Let "P" be the amount invested initially.

From the given information, P becomes 2P in 3 years.

Since the investment is in compound interest, for the 4th year, the principal will be 2P.

And 2P becomes 4P (it doubles itself) in the next 3 years.

Therefore, at the end of 6 years accumulated value will be 4P.

So, the amount deposited will amount to 4 times itself in 6 years.

**Related Topics :**

Apart from the stuff given in this section, if you need any other stuff in math, please use or google custom search here.

HTML Comment Box is loading comments...

You can also visit the following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**