3.1
Determine if the function is one-to-one:
f(x) = x^3-2x
Yes, it's one-to-one (passes horizontal line test).
Graph
f(x) = 2^x+3
" Find the domain, range, asymptote"
"Domain : " (-oo, oo)
"Range : " (3,oo)
"Asymptote : " y = 3
Simplify
log_3(81) - ln(e^2)
2
Expand
log_3(6xy^2)
log_3(6)+log_3(x)+2log_3(y)
Solve
5e^(2x)=35
x = ln(7)/2
Suppose that $18,000 is invested in a bond fund and the account grows to $23,344.75 in 5 yr
"Use the model " A=Pe^(rt) " to determine the average rate of return "
"under continuous compounding. Round to the nearest tenth of a percent."
r = 5.2%
Given
h(x) = x-7//4 ", find " h^-1(x)
h^-1(x) = 4x + 7
Polo borrows $5000 for 6 years, he has the option to do a simple interest at 6% or do a compounded continuously at 5.5%, which option would be greater?
"Simple = 1800"
"Continuous = 1882.07"
"Continuous would be greater"
Graph
f(x) = log_5(x+1) - 2
"State domain, range, and asymptote"
"Domain : " (-1,oo)
"Range : " (-oo,oo)
"Asymptote : " x = -1
Simplify
3log_2(x)-2log_2(y)
log_2(x^3 / y^2)
Solve
log_4(x-1)+log_4(x+1)=1
x = +- sqrt5
The population of Germany in 2011 was approximately 85.5 million.
"The model " P=85.5e^(-0.00208t) " represents a short-term "
"model for the population, t years after 2011."
"a) Based on the model, is the population of Germany increasing or decreasing?"
"b) Determine the number of years after 2011 at which the population of "
"Germany would decrease to 80 million if this trend continues. Round to the nearest year."
a. decreasing
b. 32 yr
Is the function
f(x) = sqrt(x+3) " one-to-one?"
"Write the domain, range, and its inverse."
Yes, it's one-to-one
"Domian :" [-3,oo), "Range :"[0,oo)
"Inverse : " f^-1(x) = x^2 - 3
Eddy starts off with $3000 at 4.5% compounded monthly for 5 years, after 5 years where would his amount be at?
"Amount = 3746.14"
Convert:
"a) " log_7(x) = 3
"b) " 2^y = 16
"a) " 7^3= x
"b) " log_2(16) = y
Expand
ln((xy)^2/z^3)
2ln(x) + 2ln(y) - 3ln(z)
A $2500 bond grows to $3729.56 in 10 yr under continuous compounding. Find the interest rate. Round to the nearest whole percent.
4%
A lab starts with a bacteria culture containing 500 bacteria. The population doubles every 3 hours.
"a) Write a function of the form " P(t) = P_0e^(kt) " to model the population P(t) after t hours"
"b) How many bacteria will there be after 9 hours?"
"c) After how many hours will the population reach 8000 bacteria? Round to the nearest tenth."
"a) " P(t) = 500e^(0.2310t)
"b) " 3996.5
"c) 12 hours"