Exponential Growth and Decay

Essential Question

• How does exponential growth differ from exponential decay and how do I find the rate of change?

Exponential Functions

• An exponential function has an x in the exponent (and numerical values everywhere else).

• y = a•bx

– Coefficient: a– Base: b– Exponent: x

The base determines growth or decay.• Put y = 3(2)x into y1 in your calculator and

graph.• Does it look like it will be growth or decay?

Why? Share with a partner.

It is growth because as x values increase, y values also increase.

What is the b value (base) in this equation?2

• Now put y = 3(1/2)x into y1 in your calculator and graph.

• Does it look like it will be growth or decay? Why? Share with a partner.

It is decay because as x values increase, y values decrease.

What is the b value (base) in this equation?1/2

So…….

• If the base “b” is greater than 1, the function will be exponential growth.

• If the base “b” is less than 1 (but always greater than 0), the function will be exponential decay.

On your whiteboard:(((Remember: y = a•bx)))

y = 5x

• a = _____ (y-intercept)• b = _____ (base value)• Growth or decay? _________

15

growth

On your whiteboard:(((Remember: y = a•bx)))

y = (0.4)x

• a = _____ (y-intercept)• b = _____ (base value)• Growth or decay? _________

10.4

decay

On your whiteboard:(((Remember: y = a•bx)))

y = 8(0.25)x

• a = _____ (y-intercept)• b = _____ (base value)• Growth or decay? _________

80.25

decay

On your whiteboard:(((Remember: y = a•bx)))

y = 4(2.5)x

• a = _____ (y-intercept)• b = _____ (base value)• Growth or decay? _________

42.5

growth

On your whiteboard:(((Remember: y = a•bx)))

y = 1/2(3)x

• a = _____ (y-intercept)• b = _____ (base value)• Growth or decay? _________

1/23

growth

On your whiteboard:(((Remember: y = a•bx)))

y = 50(1.01)x

• a = _____ (y-intercept)• b = _____ (base value)• Growth or decay? _________

501.01

growth

Finding the rate of growth or decay• A = C(1 ± r)x

• How can we write 3 as 1 ± r and what would r be?• Well, 3 = 1+2 so r = 2• We say this function is growing at a rate of 200%.

• How can we write 0.6 as 1 ± r and what would r be?• Well, 0.6 = 1 – 0.4 so r = 0.4• We say this function is decaying at a rate of 40%.

a b

Socrative