Exponential Growth and Decay Application of Exponential Relations Exponential Growth and Decay

EXPONENTIAL GROWTH MODEL WRITING EXPONENTIAL GROWTH MODELS Recall: EXPONENTIAL GROWTH MODEL a is the initial amount. t is the time period. y = a (1 + r)t (1 + r) is the growth factor, r is the growth rate.

EXPONENTIAL DECAY MODEL WRITING EXPONENTIAL DECAY MODELS A quantity is decreasing exponentially if it decreases by the same percent in each time period. Real life examples: rate of decay of radioactive material, decline in population EXPONENTIAL DECAY MODEL a is the initial amount. t is the time period. y = a (1 – r)t y is the Final amount. (1 – r ) is the decay factor, r is the decay rate.

Example: Depreciation You buy a new car for $22,500. The car depreciates (declines in value) at the rate of 7% per year, What was the initial amount invested? What is the decay rate? The decay factor? What will the car be worth after the first year? The second year? The initial investment was $22,500. The decay rate is 0.07. The decay factor is 0.93. t 3 1 22 500 07 20 925 ) ( , . $ y r t = - y = a ( 1 - r ) a 2 y = 22 , 500 ( 1 - . 07 ) y = $ 19460 . 25

A rubber ball bounces and reduces 10% of its initial height A rubber ball bounces and reduces 10% of its initial height. Sara drops the ball from a height of 2.5 m. What would its height be after the 4th bounce.

Special case: half-life of radioactive elements Radioactive decay is a process by which a substance made of unstable atomic nuclei decays. The time it takes for a quantity to decay (be reduced) to half its initial amount is called the half-life t h The relation for half-life is always: y = a 1 2 Where t represents the time, and h represents the half-life

An isotope of sodium, Na-24, has a half-life of 15h An isotope of sodium, Na-24, has a half-life of 15h. If a sample contains 55g of Na-24, find the amount remaining after 2 days.