Characteristics of Exponential Functions
What is line that an exponential function flattens out to, and never touches it.
Asymptote
Explanation - Asymptote is the line that exponential functions will never cross or touch. This is where these functions flatten out.
Is the equation "y=2(0.8)^x" Growth or Decay?
Decay
Explanation: The equation a(1+or- r)^x, adds or subtracts the 1. Depending on if you subtract or add is if the slope is increasing or decreasing. When it's under 1 it is decay because it is decreasing.
What value does exponential regression represent?
b/r value
Explanation: It represents growth and Decay or percentage rate.
(2^5-6x^4)^2
1024-36x^8
Explanation: When you simplify the expression uses power rule you get 1024-36^8.
√20
2√5
Explanation: simplifies to 2√5.
What does the number 6 represent in the equation: y=6(0.8)^x
Starting Value/y-intercept
Explanation: The a-value in the equation y=a(b)^x, represents the starting value which is the y-intercept on graphs.
Tim has a truck that decreases in value by 20% each year. What is the r-value?
0.8
Explanation: The r-value is depending on whether the number is decreasing or increasing. If it is decreasing you have to subtract it from one. So first you need to change the percent to decimal then subtract from one which gets 0.8.
What is the exponential regression of the table below? (round to the nearest hundredth).
x: 1,2,3,4,5,7
y: 6,9,12,15,21
1.21
Explanation: when you plug it into your calculator the calculator gives you a b-value of 1.21.
9^4x9^5
9^9
Explanation: using the product rule you get 9^9 because you add the exponents.
√24
2√6
Explanation: simplifies to 2√6.
This the domain and range correct?
Domain: {-3,-1,0,3,4,-7,10}
Range: {-2,0,4,6,3,11}
No
Explanation - The answer is no because when doing the domain and range of a discrete graph, you have to put the numbers in order from least to greatest.
A captain has a boat that he bought for 400 dollars. The boat appreciates in value each year by 15% each year. What is the Growth or Decay?
1.15
Explanation: It's growth because it's increasing in value and not decreasing. Once you find that it's growth you need to change the present into a decimal then add it to one which gives you 1.15.
What's the exponential regression of the table below? (round to the nearest tenth)
x: 0,1,2,6,9
y: 50,62,76,88,94
1.1
Explanation: when you plug it into your calculator the calculator gives you a b-value of 1.1
4076/407
6
Explanation: you have to bring up the 407 then you subtract them and it equals 1 because to the power of zero is 1 then you multiply the 6x1 and get 6.
√99
3√11
Explanation: simplifies to 3√11
What is the asymptote of a line with an equation of 2(3)^x - 7
y = 7
Explanation - The asymptote is added to the end of the equation. You can also use the process of elimination because the 2 is the starting value, 3 represents the rate of change, and x represents the time.
What is the percentage of growth in the equation y=32(1.5)^x-1.75?
50%
Explanation: The r-value is the percent rate. You need to change it from decimal to percent.
What's the a-value of the table below? (round to the nearest tenth).
x: 1,3,7,15,31
y: 7,13,15,22,35
9.5
Explanation: when you plug it into your calculator the calculator gives you a a-value of 9.5
x5y10/x3y11
x2/y
Explanation: Quotient rule for exponents has you bring up the exponent of the same value and subtract. Then, negative exponent rule has you bring down the numbers with negative exponents to make them positive.
√156
2√39
Explanation: √156 simplifies to 2√39
A graph has a y-intercept at (0,8), an asymptote at y=6, and the x-intercept is at (4,0). What is the a-value in the formula: y=a(b)^x?
a=8
Explanation: A-values represent the starting value. On graphs starting values represent y-intercepts.
How many years has it been in the equation y=4(16)^2+7
2
Explanation: the x-value represents time because it is an independent variable.
What's the full equation of the table below? (round to the nearest tenth).
x: 10,15,17,21,24
y: 567, 329, 241, 105, 90
2,477.6 (0.9)^x
Explanation: when you plug it into your calculator the calculator gives you a b-value of 0.9, and an a-value of 2,477.6.
33x5y8/22x7y3
3y5/2x2
Explanation: 33 and 22 gets simplified, then you have to use the quotient rule, then use the negative exponent rule.
√500
18
Explanations: √500 simplifies to 18