## Key Concepts

- Define exponential growth
- Define exponential decay
- Solve problems involving exponential growth and decay
- Find the compound interest

### Exponential Growth and Decay

#### Exponential growth

- The graph of the exponential function is an increasing asymptote if the value of b is greater than 1.

**Example:** Graph of f(x)=2^{x}

- We can model exponential growth with a function f(x) = a.b
^{x},

#### Exponential growth

- The graph of the exponential function decreases if the value of b lies between 0 and 1.

**Example: **Graph of (1/2)^{x}

- We can model exponential decay with a function f(x) = a.b
^{x},

#### 3. Applications of exponential growth

- We can calculate the compound interest using an exponential growth function.

**Example: **If Jenny invested $350 in a bank. Find the amount she will receive after 3 years if the amount was compounded quarterly at 5%?

**Solution:** The principal amount is $350.

The rate of interest is 5% or 0.05.

The number of times per year the interest is calculated is 4.

Compound interest = 350(1+0.05 / 4)^{4×3}

= 350(1+0.0125)^{12}

= 350(1.0125)^{12}

= 350 × 1.16075451772

= 406.264081202

≈ $ 406

## Exercise

- Write an exponential growth function for the initial value of 1,250, increasing at a rate of 25%.
- Write an exponential decay function for the initial value of 512, decreasing at a rate of 50%.
- What is the difference in the value after 10 years of an initial investment of $2,000 at 5% annual interest when the interest is compounded quarterly rather than annually?
- Write an exponential function to model the data in the table.

- Find the approximate value of
*x*that makes f(x)=g(x). - f: initial value of 200 decreasing at a rate of 7%
- g: initial value of 30 increasing at a rate of 5%

### Concept Map

### What have we learned

- The graph of exponential functions where, 0<b<1 is decreasing, is called
**Exponential Decay**. - The graph of exponential functions where, b>1 is increasing, is called
**Exponential Growth**.

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