Exponents and roots

Multiplying exponents

100

x^{3 .} x⁴

x⁷

200

2^{5 .} 2³

2⁸

300

a^{2 .} a^{6 .} a

a⁹

400

(3x²)^{2 .} x³

9x⁷

500

(y³)^{4 .} y²

y¹⁴

Dividing exponents

100

x⁷/x³

x⁴

200

5⁶/5²

5⁴

300

a⁹/a⁴/a

a⁴

400

12x⁵/3x²

4x³

500

(y⁸)²/y⁵

y¹¹

Negative exponents

100

2^-3

1/8

200

a^-2b³

b³/a²

300

(2/3)^-2

9/4

400

x^{-2 .} x⁵

x³

500

(x^-3y²)²

y⁴/x⁶

Exponential growth and decay

100

What is exponential growth?

Exponential growth is when the rate of increase of a quantity is directly proportional to its current value.This means that the larger the quantity,the faster it grows.

200

What is exponential decay?

Exponential decay is the rate of decrease of a quantity is directly proportional to its current value.This means that the larger,the quantity the faster decreases.

300

A population of rabbits is 200 and increases by 20% each year.What will the population be after 3 years?

The population after 3 years will be 346 rabbits.

400

A medicine has 400 mg in the body.Each hour,30% of it is used up.How much remains after 3 hours?

After 3 hour they will be 137.2 mg remaining.

500

A town has 10,000 people,but the population decreases by 5% every year.How many people will be there after 3 year?

After 3 years there will be 8,574 people.

Compound interest

100

You invest $1,000 at 5% interest,compounded annually,for 3 years.How much will you have?

You will have $1,157.63

200

You invest $2,500 at 4% interest,compounded quarterly,for 2years.How much will you hav?

You will have $2,707.14

300

You put $3,000 into a savings account that earns 6% interes,compounded monthly,for 5 years.What is the total?

The total will be $4,046.55

400

You deposit $5,000 at 3% interest compounded semiannually.How much will you have after 4 years.

I will have $5,630.00 after 4 year.

500

How much interest is earned if $1,800 is invested at 5% compounded annualy for 6 year?

$612.18 interest earne.