Pre-Calculus 5-1 and 5-2 Growth and Decay Objective: Apply exponents

Exponential Growth Function The function is of the form: f (x) = a b x, where a > 0, b > 1, x  R. Exponential Decay Function The function is of the form: f (x) = a b x, where a > 0, 0 < b < 1, x  R.

The variations of exponential growth/decay function model is very practical in a wide variety of application problems. Growth:y = a (1 + r ) t Decay:y = a (1 – r ) t Rate r is measured as a percent Time period t is measured in years a stands for the initial amount.

You have a new computer for $2100. The value of the computer decreases by about 30% annually. a) Write an exponential decay model for the value of the computer. b) Use the model to estimate the value after 2 years and 3 months. $ y = 2100(1 -.3) t

Teen spending has grown 3.5% annually from 2006 to today. If spending was $79.7 billion in 2006, how much can we expect in 2015? a)Write the exponential growth model and estimate spending in b) Use the model to estimate spending 4 years and 9 months before T s = 79.7( ) t T s = 67.7 Billion T s = 108 Billion

Compound Interest A=P(1+r/n) nt P - Initial principal r – annual rate expressed as a decimal n – compounded n times a year t – number of years A – amount in account after t years

Compound interest example You deposit $1000 in an account that pays 8% annual interest. Find the balance after I year if the interest is compounded with the given frequency. a) annually b) quarterlyc) daily A=1000(1+.08/1) 1x1 = 1000(1.08) 1 ≈ $1080 A=1000(1+.08/4) 4x1 =1000(1.02) 4 ≈ $ A=1000(1+.08/365) 365x1 ≈1000( ) 365 ≈ $

Homework Page 173 #13, 17, 21, 25, 31 Page 178 # 15, Then pick 3 from 17 – 28 that you didn’t pick on Friday.