7­7 Exponential Growth and Decay compound interest​
(noun) KAHM pownd IN trist Related Words:​
principal (noun), simple interest (noun), interest rate (noun) Definition:​
Compound interest is interest earned on both the principal and on any interest the account has already earned that remains in the account. Essential Understanding​
An exponential function can model growth or decay of an initial amount. Identify the initial amount a and the growth factor b in each exponential function. A.) g (x) = 14 • 2x
B.) y = 25600 • 1.01x
C.) College Enrollment The number of students enrolled at a college is 15,00 and grows 4% each year . 1. The initial amount a is___. 2. The percent rate of change is 4%, so the growth factor b is 1 + __ = __. 3. To find the number of students enrolled after one year, you calculate 15, 000 • ____ . 4. Complete the equation y = ___ • ___ to find the number of students enrolled after x years. 5. use your equation to predict the number of students enrolled after 25 yr. When a bank pays interest on both the principal and the interest an account has already earned, the bank is paying ​
compound interest​
. Compound interest is an example of exponential growth. Find the balance in each account after the given period. D.) $4000 principal earning 6% compounded annually, after 5yr E.) $500 principal earning 4% compounded quarterly, after 6yr F.) $5000 deposit earning 1.5% compounded quarterly, after 3yr G.) $775 deposit earning 4.25% compounded annually, after 12yr The function y = a • bx can model ​
exponential decay​
as well as exponential growth. In both cases, b is determined by the percent rate of change. The value of b tells if the equation models exponential growth or decay. Identify the initial amount a and the decay factor b in each exponential function. H.) y = 5 • 0.5x
x
I.) g (x) = 100( 23 ) State whether the equation represents exponential growth, exponential decay, or neither. J.) y = 2 • 0.68x
K.) y = 68 • 0.2x