Exponential Functions

Front

exponential function

Back

y=ab^x

^{a = initial value (y-intercept)}

^{b= common ratio}

Front

exponential growth

Back

y=a(1+r)^t

^{a= initial value}

^{r= rate (as a decimal)}

^{t= time}

^{y= final amount}

Front

exponential decay

Back

y=a(1-r)^t

^{a= initial value}

^{r= rate (as a decimal)}

^{t= time}

^{y= final amount}

Front

compound interest

Back

Front

arithmetic explicit formula

Back

a_n=a₁+(n-1)d

a_n = nth term

a₁= first term

n= term number

d = common difference

Front

geometric explicit Formula

Back

a_n=a₁(r)^n-1

a_n = nth term

a₁= first term

n= term number

r = common ratio