Exponential Rules
Finish the exponential rule:
am ⋅ an =
am+n
What is the general exponential equation?
y= a⋅bx
What values for growth factors, b, will produce an exponential growth?
y=a⋅bx
Growth factors that are greater than 1.
b>1
What values for growth factors, b, will produce an exponential decay?
y=a⋅bx
Growth factors that are less than 1.
b<1
How can you identify the vertical intercept of a exponential graph?
To identify the vertical (y) intercept of an exponential graph, find the point where the curve crosses the y-axis, which always occurs where x=0.
Finish the exponential rule:
am ÷ an
am-n
What does the a and b represent in the general exponential equation?
A: Initial value
B: Growth Factor
In a biology lab, 500 bacteria reproduce by splitting. Every hour, on the hour, each bacterium splits into two bacteria.
a. Write an expression to show how to find the number of bacteria after two hours.
500 ⋅ 2 ⋅ 2
A new bicycle sells for $300. It is on sale for 1/4 off the regular price.
What expression represents the sale price of the bicycle in dollars?
300 ⋅ 3/4
Refer to google doc
250,000 butterflies
Simplify:
x3 ⋅ x2
x5
The value of a home in 2015 was $400,000. Its value has been doubling each decade.
a. If v is the value of the home, in dollars, write an equation for v in terms of d, the number of decades since 2015.
v=400,000(2)d
In a biology lab, 500 bacteria reproduce by splitting. Every hour, on the hour, each bacterium splits into two bacteria.
Write an equation relating n, the number of bacteria, to t the number of hours.
n=500⋅2t
At the beginning of April, a colony of ants has a population of 5,000 and decreases by 1/5 monthly.
Write an expression for the ant population at the end of May
5,000(4/5)2
Refer to google doc.
Week 1: 150,000
Week 2: 90,000
Simplify:
x5 ÷ x2
x3
The area, A, of a forest, in acres, is modeled by the equation A=5,000⋅(5/4)d where d is the number of decades since the beginning of the year 1950.
a. Is the area of the forest increasing or decreasing with time?
Increasing; Growth factor(5/4) is larger than 1.
In a biology lab, a population of single-cell parasites reproduces hourly. An equation which gives the number of parasites, p, after t hours is p=100⋅3t. Explain what the numbers 100 and 3 mean in this situation.
100: The number of initial single-cell parasites.
3: Growth factor
At the beginning of April, a colony of ants has a population of 5,000 and decreases by 1/5 monthly.
What is the ant population after 7 months?
1,048.576; approximately 1,049 ants.
Refer to the google doc.
Growth factor: 3/5
Simplify:
2x3y2 ⋅ 2x1 y4
4x4y6
Jada saw a music video that her favorite artist recently posted online. The equation v(t)=320⋅4t represents the number of views v of the video, t days since Jada saw the video.
What does the 320 and 4 represent in this equation?
320: The initial amount of views when Jada first viewed the video.
4: Growth factor
In a biology lab, a population of single-cell parasites also reproduces hourly. An equation which gives the number of parasites, p, after t hours is p=100⋅3t.
Use the equation to determine the number of parasites after 3 hours.
There will be 900 parasites after 3 hours.
A liquid level gauge is used to measure the water level in a water tank. Before the tank was emptied, the liquid level gauge read the water level of the tank as 400 centimeters. While emptying the tank, the water recedes at a rate of 100 centimeters per hour.
What is the water after 5 hours?
Water Level is at 94.921875 centimeters after 5 hours.
Refer to the google doc.
q=250,000(3/4)t