Rewriting Exponential Functions
The value y of an investment x months after the money was invested is given according to the equation below. y = 25,000(1.16)^-x As time goes on, does the value of the investment grow or decay?
decay
Which expression relates h, the number of half-lives, and y, the number of years?
h=y/2.6
What is the base of the exponential function?
0.86
How many grams of fermium will remain after twenty-three days?
1.986 g
Use what you know about negative exponents to choose the equation below that is equivalent.
2nd option
Find the frequency for the pitch E shown
659 Hz
Click here to listen to a keyboard play the notes starting at A and ending at E. Each note is a half-step above the previous note. How many half-steps are there between A440 and the E above it?
7
Approximately how many milligrams of sodium remain after 8.4 years?
85.2 mg
Choose all equivalent expression(s). ab^-3x
C. a(1/b)^3x D. a((1/b)^3)^x
Martin deposits $200 in a savings account that earns 5% annual interest. Four years later, Cary deposits $200 in an account earning the same interest. Let M represent the balance in Martin's account and let C represent the amount of money in Cary's account. Choose the pair of expressions that describe the accounts y years after Martin opened his account.
D. Martin:200(1.05)^y Cary: 200(1.05)^y-4
Which equation below compares the amount of medicine, S, in Sofia's system with the amount of medicine, L, in Lexi's system?
L=16xS
Choose the equation that relates the balances in the accounts y years after Martin opened his account.
M = 1.22C
Which of the following functions represent exponential growth?
A,B,C
What formula(s) below represents the frequency of that E? Check all that apply.
A,C,E
Abel and Zöe's grandparents opened a savings account for an equal amount upon the birth of each child. Now, the values of their accounts could be found by the following expressions, where t represents the years since 2011. Abel: y = 1266.77(1.03)t Zöe: y = 1159.27(1.03)t Based upon this information, find the difference in the children's ages. Suggestions: Find the ratio 1266.77/1159.26. What does that ratio represent in terms of powers of 1.03? You also can graph both equations and figure out the shift.
Abel is 3 years older than Zöe.
Which of the following functions represent exponential decay?
B,C,D
Choose all equivalent expression(s).
B. (4)^-3x^2 C.(1.4)^3x^2
In the previous video, you compared the two functions below. f(x)=1.2^t g(x)=1.2^t-5
B. It shifts the graph of f right 5 units. F. It divides all the y-values by 1.25.
What formula would you use to calculate the mass of fermium-253 remaining after d days?
B. f(d)=400(0.794)^d
Sofia takes 10mg of a medicine whose concentration in blood decreases by a factor of one half every day. Let t be the number of days since Sofia took the medication. The amount of medication in her system after t days is S = 10(½)t. Four days later, Lexi takes 10mg of the same medicine. How much medication, L, is in Lexi's system on day t?
C. L=10(1/2)^t-4
Fermium-253 has a half-life of three days. A sample contains 400 g. How long will it take for the sample to decay to 100 g?
Number of half-lives: 2 Number of days: 6 How many grams of fermium will remain after fifteen days? 12.5
The half-life of sodium-22 is 2.6 years. A sample contains 800 mg of this isotope. Which expression represents the mass of sodium remaining after h half-lives?
S = 800(0.5)^h
Combine the first two equations and laws of exponents to find the equation for the mass of sodium remaining after y years.
S = 800(0.766)^y
Here is the function for the number of zombies, N, after t years, with the negative exponent expressed using the fraction ½: N(t) = 300 • 0.5t/8 What is the half-life for the zombie population? Explain in terms of exponents. (To type an exponent, use the ^ key.)
Sample Answer: Eight years. To get ½ of the 300, you need 0.5^(t/8) to equal ½, or 0.5. That means that the exponent must be 1. This happens when t = 8 years. Check all facts you included in your answer. -The exponential part of the expression needs to be equal to ½, or 0.5. -The half-life time will occur at the value of t that gives an exponent of 1. -The value t = 8 causes the exponent to be 1, so that's the half-life.
he function below represents the number of zombies, N, where t is the number of years since the zombies gained control of Earth: N(t) = 300 · 2-t/8 Is this exponential growth or decay? Explain using your understanding of the properties of exponents. (To type exponents, use the ^ key.)
Sample Answer: This is decay. The exponent has a negative sign. The reciprocal of 2 is 0.5. So N(t) can be rewritten as 0.5^(t/8). The base is fraction less than 1, which is decay. Check all facts you included in your answer. -The negative exponent means that you must take the reciprocal of the base 2. -The reciprocal of 2 is 0.5 (or ½). -The base 0.5 (or ½) is less than 1. -Bases less than 1 cause decay.
