Chapter 4 Exponential Functions Flashcards
What is the exponential function?
It is a function of the form
f(t)=ab^t
What is the initial value of the exponential function?
f(t)=ab^t
The “a” value
What is the growth factor of the exponential function?
f(t)=ab^t
The “b” value
What is the growth rate in the exponential function?
f(t)=ab^t
Since b=1+r, the “r” value is the growth rate.
When is the Exponential function growing?
When r > 0 and b > 1
When is the exponential function decaying?
When r < 0 and 0 < b < 1
What is the difference between exponential and linear functions?
The difference is that a linear function will have consecutive values with the whole number difference between them being constant.
Consecutive exponential values have constant percentage differences rather than whole number ones
What does the “a” value in an exponential function tell us?
It tells us the y-intercept of the function
What does the “b” value in an exponential function tell us?
It tells us the concavity of the function.
Concave up for growth and Concave down for decay
How would you express a horizontal asymptote in function form?
f(x) —> k as x —> infinity
Or
f(x) —> k as x —> negative infinity
What is the nominal interest rate?
The annual interest rate
What is the effective interest rate?
The actual earned interest when the interest is compounded more frequently than once a year
What is the effective annual interest rate of an account that pays interest at the nominal rate of 6% per year compounded daily and hourly?
To do this, you would need to first divide the annual interest rate by the amount of times per year the interest is applied
For daily
0.06/365 = 0.061831
Then add one to get the result
1.061831
Do the same thing for the hourly rate
What is the formula to find out the effective rate of return?
B=P(1+(r/n))^nt
Where n is the amount of times per year that the interest is applied.
What is “e”?
It is the irrational euler number with an approx value of 2.71828…
