Sequences
List the first 5 terms of a sequence with an initial value of 4 and a common difference of 3.
4, 7, 10, 13, 16
What is the domain of any exponential function?
(-∞,∞)
What is the initial value, growth factor, and growth rate of this function, f(x)=400(1.40)x
Initial value: 400 Growth factor: 1.40
Growth rate: .40 or 40%
Rewrite the explicit formula for this geometric sequence as an exponential function.
an=8(3)n-1f(x)=8(3)x
What forrmula do we use for something that is compound continuously?
A(t)=Pert
Write the explicit and recursive formula for this sequence.
100, 20, 4, .8, ...
Recursive
a1=100
an=an-1(1/5)
Explicit
an=100(1/5)n-1
Find the domain, range, asymptote, and y-intercept of the function f(x)=4(8)x+3
Domain: (-∞,∞) Range: (3,∞)
Asymptote: y=3 y-intercept: (0,7)
Which of the following functions are growth functions?
f(x)=500(1.01)x g(x)=2(0.1)x h(x)=e(2)x
j(x)=0.5(1/2)x l(x)=20(π)x m(x)=350(0.99)x
f(x), h(x), and l(x)
Write a basic exponential function increasing over (-∞ ,∞ ) and a reference point of (1,4).
y=4x
Jake invests $1,000 into his savings account that has an interest rate of 2.5% compounded quarterly for 5 years. What would the formula be for Jake's money.
A(t)=1000(1+0.025/4)4(5)
Write the 11th term of this sequence.
1024, 512, 256,...
a11=1
What does an asymptote mean/do?
An asymptote is the invisible line that the graph cannot cross/touch, the graph will approach but won't touch that value. The asymptote affects the range and end behaviors of an exponential function.
What is the initial value, growth factor, and growth rate of this function?
p(x)=35e-0.4x
Initial Value: 35 Growth Factor: 0.6703
Growth Rate: -0.3297
A town has a population of 17000 and grows at 4% every year. What will be the population after 5 years, to the nearest whole number?
20,683 people
Hudson invested $8,400 in an account paying an interest rate of 5.4% compounded quarterly. Assuming no deposits or withdrawals are made, how much money would be in the account after 13 years?
$16,869.98
What is the sum of the first 15 terms in this sequence. Round to the nearest whole number.
an=100(.6)n-1
S15=250
Write the function g(x) that transforms f(x)=3x, so that f(x) is reflected across the y-axis, vertically compressed bafo 1/2, and vertically translated down 4 units.
g(x)=(1/2)(3)-x-4
Which function has grows the fastest?
f(x)=100(1.1)x g(x)=2e0.4x h(x)=20(2)x/2
g(x)
Growth factor: g(x)=1.492 h(x)=1.414
Write an exponential function that goes through the points (-1,1) and (2,27)
y=3(3)x
Penelope invested $32,000 in an account paying an interest rate of 7% compounded continuously. Assuming no deposits or withdrawals are made, how much money would be in the account after 14 years?
$85,262.60
What is the explicit formula for the sequence and what is the 10th term?
2,_,_,-54,...
an=2(-3)n-1
a10=−39366
For the function f(x)=5(4)x-2+8, what are the domain, range, asymptote, concave up or down, end behaviors, and intervals of increasing/decreasing?
Domain: (-∞ ,∞) Range: (8,∞)
Asymptote: y=8 Concave Up
As x -> ∞, f(x) -> ∞ As x -> -∞, f(x) ->8
Increasing (-∞ ,∞)
What is the initial value, growth factor, and growth rate?
r(x)=3(4)-x/2
Initial Value: 3 Growth Factor: 1/2
Growth Rate: -1/2
An element with mass 780 grams decays by 17.1% per minute. How much of the element is remaining after 19 minutes, to the nearest tenth of a gram?
22.1 grams.
Aaden invested $840 in an account paying an interest rate of 2.75% compounded continuously. Justin invested $840 in an account paying an interest rate of 2.625% compounded daily. After 13 years, how much more money would Aaden have in his account than Justin, to the nearest dollar?
Aaden has $1200.99 and Justin has $1181.62. Aaden has $19 more. ($19.37)