7.1 Exponential Growth and Decay and Graphing Exponential Functions
State the domain and range, then make a table of values. y=3x
x y=3x
-3 y=3-3 =1/27
-2 y=3-2 = 1/9
-1 /2 y=3-1/2 = square root 3/3
0 y=30 = 1
1 y=31 =3
3/2 y=33/2 = square root 27
2 y=32 = 9
Domain and Range: All Real numbers
solve for x
2x=83
x=9
25=32
log232=5
Evaluate.
log232
5
Find the multiplier for each rate of growth or decay.
a. 8% growth
b. 0.05% decay
a. 1.08
b. .995
Graph and make a table: y=2x+1
Answer with Tara and Clara
Kristen starts an experiment with 7500 bacteria cells. After 4 hrs, there are 23,000 cells. Write an exponential function that could be used to model the number of bacteria after x hours if the number of bacteria changes at the same rate.
function: 23000=75000 x b4
b=1.323
Write the logarithmic equation in exponential form.
log255=12
251/2=5
Use log43 = 0.7925 to approximate the value of log4192
= 3.7925
State the domain and range of the asymptote.
f(x)=2x-1
Domain: all real numbers
Range: y greater than -1
Asymptote: y greater than -1
Suppose you invested 1000 in a company's stock at the end 2005 and the value of the stock increased at a rate of 15% per year. Predict the value of the stock, to the nearest cent, at the end of the years 2010 and 2015.
2010: 2011
2015: 4045
Find the final amount of a 500$ investment after 8 years at 7% interest compounded annually, quarterly, monthly, and daily.
annually: $859.093
quarterly: $871.11
monthly: $873.91
daily: $875.96
Evaluate each expression
a. log416
b. log61/2 16
a. x=2
b. x=-3
given log25 = 2.3219 approximate the value of log210
= 3.3219
Solve the equation for x.
logx216=3
x=6
Suppose you buy a new car for 15000 and its value decreases at a rate of about 8% per year. Predict the value of the car, to the nearest cent, after 4 years and after 7 years.
4 years: 10,745.9
7 years: 8,367.70
What is the formula for compound growth?
A(t)=P (1+r/n)nt
log8(3x-7)=log8(48-8x)
x=5
Use the power property of logarithms to evaluate the following
36
Evaluate to the nearest hundredth.
1-log521
-0.892
The function P(x)=2.28(0.9x) can be used to model the number of pay phones in millions of x years since 1999. Classify the function as either exponential growth or decay, and identify the growth or decay factor.
decay of 0.9
An investment account pays 4.2% annual interest compound monthly. If $2500 is invested in this account, what is the balance in 15 years?
$4688.87
log2(x2-4)=log23x
x=4
Express log320 in terms of common logarithms, then round to the nearest ten-thousandth.
2.72
Evaluate.
3log7x + 2log7(3y) + log7w
log7x3 x 9y x w