Exponential Growth, Decay, or Neither
Determine if the following function is an Exponential Growth, Decay, or Neither.
y=15*9^x
Exponential Growth
Solve the following equation for x:
2^x=32
x=5
What is the domain for all exponential functions?
(-oo,oo)
A bunny population doubles every 6 months. Researchers wonder what the population will be in 3 years if there are currently 10 bunnies. What is the initial population? What is the growth factor?
Growth Factor: 2
The population of deer in a forest, P, is a function of the number of years, t, since the population was first recorded. This relationship can be represented by the equation P=420(1.06)^t . What does 1.06 represent in this context?
1.06 represents the growth factor, showing that the population grows by a factor of 1.06 per year.
Determine if the following function is an Exponential Growth, Decay, or Neither.
y=-13x^8
Solve the following equation for x:
4^x=4096
x=6
What feature of an exponential function do you need to know and identify on a graph to help identify the range?
Horizontal Asymptote
A 40-pound pile of compost decreases in weight by 12% each week. If f(t) is the weight of compost after t weeks, write an equation to model this situation.
f(t)=40(1-0.12)^x or
f(t)=40(0.88)^t
A vine is 24 inches long. If the plant grows by 20% each year, how long will the vine be in 5 years? Round to the nearest hundredth.
59.72 inches
Determine if the following function is an Exponential Growth, Decay, or Neither.
y=11*(1/9)^x
Exponential Decay
Solve the following equation for x:
5^(x+3)=5^(2x-1)
x=4
Find the domain, range, and y-intercept of the following function:
Domain and Range need to be in interval notation and the y-intercept needs to be listed as an ordered pair.
f(x)=5.1556^x
Domain: (-oo,oo)
Range: (0,oo)
y-intercept: (0,1)
The population of deer in Yosemite Valley in 2019 is 18,600 and has an annual growth rate of 7% per year. If g(t) is the number of deer in Yosemite Valley after 2019, write an equation to model this situation t years after 2019.
g(t)=18600(1+0.07)^t or
g(t)=18600(1.07)^t
Annual sales of a fast food restaurant are $530,000 and increasing at a rate of 5%. What will the annual sales be in 6 years? Round to the nearest cent.
$710,250.69
Given the following function: C(x)=72*(1.32)^x does this function increase or decrease over time?
Increase
Solve the following equation for x:
27^(2x)=9^(x+2)
x=1
Find the domain, range, and y-intercept of the following function:
Domain and Range need to be in interval notation and the y-intercept needs to be listed as an ordered pair.
f(x)=7(3)^x
Domain: (-oo,oo)
Range: (0,oo)
y-intercept: (0,7)
The cost of tuition at a college is $12,000 and is increasing at a rate of 6% per year.
a. What is the function, f(x) that represents this situation?
b. What will be the cost in 17 years? Round to the nearest cent.
a. f(x)=12000(1.06)^x or f(x)=12000(1+0.06)^x
b. $32,313.27
Suppose you deposit $100.00 into a bank with 6% interest compounded annually. The amount in the account after t years is given by A(t)=100(1.06)^t (in dollars)
a. What is the amount in the account after 6 years? Round to the nearest cent.
b. How long would it take the account to reach $1,500? Round to two decimals.
a. Approximately $141.85
b. Approximately 46.48 years
In the exponential function y=ab^x , which part determines an exponential growth or decay? What are the boundaries of that part?
b determines exponential growth or decay.
b>1 : Exponential Growth
0<b<1 : Exponential Decay
Solve the following equation for x:
8^(5x)=4^(x+2)
x=4/13
Find the domain, range, and y-intercept of the following function:
Domain and Range need to be in interval notation and the y-intercept needs to be listed as an ordered pair.
f(x)=5(2)^x-7
Domain: (-oo,oo)
Range: (-7,oo)
y-intercept: (0,-2)
The population of a town is 18,000 and is decreasing at a rate of 2% per year.
a. What is the function, g(x) that best represents this situation?
b. What is the population after 3 years? Round to the nearest whole number.
a. g(x)=18000(1-0.02)^x or
g(x)=18000(0.98)^x
b. 16,941 people
What is the Compound Interest Formula and what do all parts of the formula represent?
A=P(1+(r/n))^(nt)
P: represents the principal amount (initial amount)
r: represents the interest rate (as a decimal)
n: how many times it's compounded in a year/how many times it occurs in a year.
t: number of years