Exponential Function Recursive and Explicit Formulas

Quadratic

Linear

Exponential Growth

Exponential Decay

a linear function

an exponential function

a quadratic function

$$y=\frac{1}{3}\ \left(3\right)^x$$

$$y\ =\ 1\left(3\right)^x$$

f(x)= 3 f(x-1) , f(1) = 1

f(x)=f(x-1) + 3 , f(0) = 1/3

Linear

Quadratic

Exponential Growth

Exponential Decay

f(1) = 3

f(0) = 3

f(n) = f(n - 1)  * 4

f(0) = 4

f(n) = f(n - 1)  * 3

f(1) = 3
f(n) = f(n - 1)  + 9

y = 1⁄3 (3)^x ; (0, 1⁄3)

y = 1⁄3 (3)^x ; (0, 3)

y = 3 (1/3)^x ; (0, 1⁄3)

y = 3 (1/3)^x ; (0,3)

12, 48, 192, 768

12, 144, 1728, 20736

12, 24, 36, 48

3, 12, 48, 192

Decrease

Increase

a_n = 2(11)^n-1

a_n = 11x2

a_n = 11(2)^n-1

a_n+1 = a_{n *} 2;  a₁ = 11