Exponential Growth and Decay

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Presentation transcript:

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? _________ 1 5 growth

On your whiteboard: (((Remember: y = a•bx))) y = (0.4)x a = _____ (y-intercept) b = _____ (base value) Growth or decay? _________ 1 0.4 decay

On your whiteboard: (((Remember: y = a•bx))) y = 8(0.25)x a = _____ (y-intercept) b = _____ (base value) Growth or decay? _________ 8 0.25 decay

On your whiteboard: (((Remember: y = a•bx))) y = 4(2.5)x a = _____ (y-intercept) b = _____ (base value) Growth or decay? _________ 4 2.5 growth

On your whiteboard: (((Remember: y = a•bx))) y = 1/2(3)x a = _____ (y-intercept) b = _____ (base value) Growth or decay? _________ 1/2 3 growth

On your whiteboard: (((Remember: y = a•bx))) y = 50(1.01)x a = _____ (y-intercept) b = _____ (base value) Growth or decay? _________ 50 1.01 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

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