Exponent rules
State rule and answer
12x-8x
Adding/Subtracting Monomials
4x
Convert to log form:
34=81
Log3(81)=4
Does the function model exponential growth or exponential decay?
f(x) = 3 x (7/4)x
exponential growth
A local hospital receives a shipment of 80 milligrams of a specific medical isotope. The isotope is highly unstable and loses exactly half of its mass every day. How much of the isotope is left after 3 days?
10 milligrams
Simplify:
(x4y3) (x6y8)
Answer: x10y11
State the rule and the answer
(K2)(K9)
it is product rule
K11
Solve:
4x=30
x=2.4534
Does the function model exponential growth or exponential decay?
g(t)= 1.7 x 0.8t
exponential decay
A new car costs $32,000. It depreciates at a rate of 15 years every year. What is the value of the car after 4 years?
After 4 years, the car will be worth $16,704.
Simplify:
(x3)2
x6
State rule and answer
22x6/11x3
it is quotient rule
2x3
K(f)=32(0.75)f
Rewrite the equation in terms of K(f)
log0.75(k(f)/32)=f
A phone sells for $600 and loses 25% of its value per year. State whether this model is exponential decay or exponential growth. Then write a function that gives the phone's value, V(t), t years after it is sold.
V(t) = 600 x (0.75)t
A high-end laptop is purchased for $1,200. Each year, it loses 20% of its value. Calculate the value of the laptop after 4 years.
V(4) = $491.52
Simplify:
(3/4)-5
1024/243
state the rule and the answer
(B5)3
It is power rule
B15
State rule and answer:
log484 - log412
Rule: quotient rule
Answer:log4(7)
A biologist has a sample of 6000 cells. The biologist introduces a virus that kills 1/3 of the cells every week. Write a function that gives the number of cells remaining C(t) in the sample t weeks after the virus is introduced.
Hence, find how many cells remain after 9 weeks.
C(t)= 6000 x (2/3)9
C(9)= 156.073769
The population of mosquitoes decreases exponentially. The size of the population, P, after t days is modeled by P = 3200(2)^-t+50, where t>0. (a) Write down the exact size of the initial population.
(b) Find the size of the population after 4 days. (c) Calculate the time it will take for the size of the population to decrease to 60. (d) The population will stabilize when it reaches a size of k. Write down the value of k.
(a) 3250
(b) 250
(c) approximately 8.32 days
(d) 50
Simplify:
(2x3y-2)3/4x-1y5
2x10y-11 or 2x10/y11
state the rule and answer
(w6)2/w12
Zero exponent rule
w12/w12= w0= 1
Solve:
40(5)x-10=515
x=1.5996
You invest $500 in a savings account that pays 3% compound interest annually. How much money will you have after 5 years?
$579.64
A fast-growing tech startup launches a new streaming platform with 50,000 initial subscribers. The marketing team tracks user acquisition data and finds that the subscriber base doubles every 3 years. If this growth rate remains steady, how many years will it take for the platform to reach exactly 200,000 subscribers?
Use the formula, A(t) = A0 x 2^(t/d), where A(t) is final population, A0 is initial population, d is doubling time cycle, and t is total time passes in years.
6 years
Simplify:
(x2y-3/x-4y5)-2
y16/x12 or x-12y16