Exponential Graphs
Will the following function exhibit growth or decay?
y=2(0.4)^x-5
Decay
A robot vacuum cleans a dirty floor using multiple passes. During each pass, 15% of the dirt is removed. If the floor initially has 16 oz of dirt, write an equation to represent the situation using x and y.
y=16 (0.85)^x
Ndiba invests $1,933 in a savings account with a fixed annual interest rate of 3% compounded biannually. What will the account balance be after 10 years?
$2,603.47
Solve the following equation.
5 ^ (3m - 3) = 5 ^ (-2m - 2)
m=1/5
Given the following function, determine the starting value:
y=4(1/2)^x
4
Will the following function exhibit growth or decay?
y=0.3(5)^x+1
Growth
A company promises to release a new smartphone model every month. Each model's battery life will be 5% longer than the previous model's. If the current model's battery life is 610.0 minutes, what will the latest model's battery life be 9 months from now? Round to the nearest tenth.
946.3 minutes
Anjali invests $4,082 in a retirement account with a fixed annual interest rate of 5% compounded continuously. What will the account balance be after 15 years?
$8,641.59
Solve the following equation:
4 ^ (-2n) = 16
n=-1
Given the following function, list the multiplier.
y=0.5(3)^x
What is the domain for the following function?
y=2^x
(-oo,oo)
A philanthropist pledges to donate 14% of a fund each year. If the fund initially has $421,000, how much will the fund have after 12 years? Round to the nearest penny.
$68,907.03
Jaidee invests $8,644 in a savings account with a fixed annual interest rate of 6% compounded quarterly. What will the account balance be after 12 years?
$17,663.83
Solve the following equation:
625 ^ (2 - 2a) = 25 ^ (-3a)
a=4
What is the percentage growth rate for the given equation? (Answer must be listed as a %)
y=4000(1.07)^x
7%
Determine the horizontal asymptote for the given function:
y=4(.2)^x-7
y=-7
A rubber bouncy ball is dropped from a height of 114.00 inches onto a hard flat floor. After each bounce, the ball returns to a height that is 16% less than the previous maximum height. What is the maximum height reached after the 12th bounce? Round to the nearest hundredth.
14.07 inches
Kathryn invests $5,973 in a savings account with a fixed annual interest rate of 6% compounded monthly. What will the account balance be after 5 years?
$8,056.68
Solve the following equation:
64 ^ (x + 2) = 1 / 4
x=-7/3
What is the percent decrease for the given equation? (Answer must be listed as a %)
y=250(0.85)^x
15%
Determine the y-intercept for the given equation:
y=2(3)^x-1
(0,1)
A new social media site is increasing its user base by approximately 3% per month. If the site currently has 22,650 users, what will the approximate user base be 18 months from now? Round to the nearest whole number.
38,560 users
Jack invests $4,504 in a savings account with a fixed annual interest rate of 3% compounded continuously. How long will it take for the account balance to reach $5,900.08?
9 years
Solve the following equation:
27 ^ (-3r - 1) = 1 / 9
r=-1/9
Write an example of a function that would exhibit exponential decay.
Multiplier must be between 0 and 1