Math Test 4
Find the amount A in dollars of $2000 invested for 30 years at 8% compounded continuously. (Enter a number. Round answer to the nearest cent.) help: 0.02[x]30=[shift][in][x]2000[=]
$22046.35
. So if $200 is invested at an interest rate of 5% compounded quarterly, then the amount after 3 years is? (Round your answer to the nearest cent.)
$232.15
So if $200 is invested at an interest rate of 8% compounded continuously, then the amount after 5 years is? (Round your answer to the nearest cent.)
$298.36
Find the amount in the account after $700 is invested for 1 year at 9% compounded monthly. (Enter a number. Round your answer to two decimal places.)
$765.66
Find the amount in the account after $900 is invested for 1 year at 7% compounded monthly. (Enter a number. Round your answer to two decimal places.)
$965.06
x^4 + 9x^3 < x + 9
(-9,1)
f(x)=log3(x^2-9) f(x)=log10(x+7)
(-oo,-3)u(3,oo) (-7,oo)
(x − 8)(x + 9)(7x + 9) < 0
(-oo,-9)U(-9/7,8)
If $10,000 is invested at an interest rate of 2% per year, compounded semiannually, find the value of the investment after the given number of years. (Round your answers to the nearest cent.) - 5 years - 10 years - 15 years
- 5 years (11046.22) - 10 years (12201.90) - 15 years (13478.49)
log4(0.125) ln(e^8) ln(1/e)
-1.5 8 -1
log2(1/8) log8(square root of 8) log8(0.125)
-3 1/2 -1
log9(1) log3(1)
0
Use the Change of Base Formula and a calculator to evaluate the logarithm, correct to six decimal places. Use either natural or common logarithms. - log base 17 (2.8)
0.363410
Use the Change of Base Formula and a calculator to evaluate the logarithm, correct to six decimal places. Use either natural or common logarithms. - log base 7 (4)
0.712414
log(8) log(40.1) log(3/4)
0.9031 1.6031 -0.1249
Use the Laws of Logarithms to evaluate the expression. - 1/5 log base 3 (243)
1
log2(2) log3(3)
1
If $1000 is invested at an interest rate of 2.75% per year, compounded quarterly, find the value of the investment after the given number of years. (Round your answers to the nearest cent.) 1year, 2year, 8 year
1 year ($1027.78) 2 years ($1056.34) 8 years ($1245.14)
An investment of $5000 is deposited into an account in which interest is compounded continuously. Complete the table by filling in the amounts to which the investment grows at the indicated times. (Round your answers to the nearest cent.) r = 4%, 1-6 years
1 year ($5204.05) 2 year ($5416.44) 3 year ($5637.48) 4 year ($5867.55) 5 year ($6107.01) 6 year ($6356.25)
An investment of $3000 is deposited into an account in which interest is compounded continuously. Complete the table by filling in the amounts to which the investment grows at the indicated interest rates. (Round your answers to the nearest cent.) t = 5 years, 1%-6%
1% ($3153.81) 2% ($3315.51) 3% ($3485.50) 4% ($3664.21) 5% ($3852.08) 6% ($4049.58)
An investment of $4000 is deposited into an account in which interest is compounded monthly. Complete the table by filling in the amounts to which the investment grows at the indicated interest rates. (Round your answers to the nearest cent.) t = 5 yr, 1%-6%
1%($4205) 2%($4420.32) 3%($4646.47) 4%($4883.99) 5%($5133.43) 6%($5395.40)
For a certain type of tree the diameter D (in feet) depends on the tree's age t (in years) according to the logistic growth model D(t) = 5.41 + 2.9e^−0.01t Find the diameter of a 17-year-old tree. (Round your answer to three decimal places.)
1.567ft
log(50) log(square root of 3) log(3 times square root of 3)
1.6990 0.2386 0.7157
ln(7) ln(26.4) ln(9 + square root of 11)
1.9459 3.2734 2.5109
g(x) = 1/3^x + 1 (Round your answers to three decimals.) 1/2, -4.5, -1.5, square root of 3
1/2 = 0.192 square root of 3 = 0.050 -4.5 = 46.765 -1.5 = 1.732
f(x) = 7^x − 1 1/2 1.5 -1 1/4
1/2 =0.378 1.5 =2.646 -1 =0.020 1/4 =0.232
When a certain medical drug is administered to a patient, the number of milligrams remaining in the patient's bloodstream after t hours is modeled by D(t) = 50e^−0.2t. How many milligrams of the drug remain in the patient's bloodstream after 5 hours? (Round your answer to one decimal place.)
18.4 mg
log9(81) log7(49) log9(9^11)
2 2 11
If $1500 is invested at an interest rate of 4.5% per year, compounded continuously, find the value of the investment after the given number of years. (Round your answers to the nearest cent.) 2years, 4 years, 12 years
2 years ($1641.26) 4 years ($1795.83) 12 years ($2574.01)
Use the Laws of Logarithms to evaluate the expression. log base 2 (96) - log base 2 (12)
3
ln(31) ln(8.69) ln(62.3)
3.4340 2.1622 4.1320
Express the equation in exponential form. log3(1)=0
3^0=1
Express the equation in exponential form. log3(81)=4
3^4=81
Use the Laws of Logarithms to evaluate the expression. log(50)+log(200)
4
log5(5^4) log3(3^2)
4 2
log4(256) log6(6^7) log5(125)
4 7 3
Use the Change of Base Formula and a calculator to evaluate the logarithm, correct to six decimal places. Use either natural or common logarithms. - log base 4 (587)
4.598608
Use the Laws of Logarithms to evaluate the expression. - log (X^4Y^2/Z^8)
4log(x)+2log(y)-8log(z)
If $3000 is borrowed at a rate of 3.75% interest per year, compounded quarterly, find the amount due at the end of the given number of years. (Round your answers to the nearest cent.) 5 years, 7 years, and 9 years
5 years ($3615.53) 7 years ($3895.76) 9 years ($4197.71)
ln(5)=7y ln(t+9)=-1
5=e^7y t+9=e^-1
4^log4(8) 5^log5(22) e^ln(20)
8 22 20
Convert the following to exponential form. log9(1/9)=-1
9^-1=1/9
Convert the following to exponential form. log9(1/81)=-2
9^-2=1/81
Convert the following to exponential form. log9(3)=1/2
9^1/2=3
Convert the following to exponential form. log9(9)=1
9^1=9
Convert the following to exponential form. log9(81)=2
9^2=81
Convert the following to exponential form. log9(729)=3
9^3=729
A radioactive substance decays in such a way that the amount of mass remaining after t days is given by the function m(t) = 12e^−0.016t where m(t) is measured in kilograms. (a) Find the mass at time t = 0. (b) How much of the mass remains after 47 days? (Round your answer to one decimal place.)
A = 12kg B = 5.7kg
COMPOUND FREQUENCY -annually -semiannually -quarterly -monthly -weekly -daily
VALUE OF N annually- 1 semiannually- 2 quarterly- 4 monthly- 12 weekly- 52 daily- 365
To solve a polynomial inequality, we factor the polynomial into irreducible factors and find all the real ______ factors intervals numbers points zeros of the polynomial. Then we find the intervals determined by the real ______ factors intervals numbers points zeros and use test points in each interval to find the sign of the polynomial on that interval.
Zeros; Zeros
If $500 is invested at an interest rate of 4.5% per year, find the amount of the investment at the end of 12 years for the following compounding methods. (Round your answers to the nearest cent.) annually, semiannually, quarterly, continuously
annually ($847.94) semiannually ($852.88) quarterly ($855.42) continuously ($858.00)
y=log5(x-2)-1 domain range asymptote
domain(2,oo) range(-oo,oo) x=2
Use the Laws of Logarithms to combine the expression. 3ln(2)+2ln(x)-1/2ln(x+3)
ln(2^3X^2/(x+3)^1/2)
Use the Laws of Logarithms to combine the expression. 1/2log base 2 (3)- 2log base 2 (5)
log base 2 (square root of 3/25)
Use the Laws of Logarithms to combine the expression. log base 3 (x^2-1) - log base 3 (x-1)
log base 3 (x^2-1/x-1)
log base 4 (2) + 2 log base 4 (5)
log base 4 (50)
Use the Laws of Logarithms to combine the expression. log base 4 (2) + 2 log base 4 (7)
log base 4 (98)
log base b (x^2-1)-log base b (x-1)
log base b (x+1)
log base x + log(x^2-49)-log5-log(x+9)
log x(x^2-49)/5(x+9)
3log(x)-4log(x+1)
log((x^3/(x+1)^4))
combine to get: 2log(x)+log(y)-log(2)
log(x^2Y/z)
Use the Laws of Logarithms to combine the expression. 4log(x)-1/4log(x^2+1)+2log(x-1)
log(x^4(x-1)^2/4square root x^2+1)
Express the equation in logarithmic form. 10^2 = 100
log10(100)=2
Express the equation in logarithmic form. 6^-2=1/36
log6(1/36)=-2
Let's solve the exponential equation 6^1-x=7
x= -0.086033
Use a calculator to find an approximation to the solution rounded to six decimal places e^1-8x=6
x= -0.098970
Solve for x. 5^x-1=6
x= 1 + ln6/ln5
Solve the logarithmic equation for x. (Enter your answers as a comma-separated list. Round your answer to the nearest whole number.) ln(x)=12
x= 162755
Solve the logarithmic equation for x. (Enter your answers as a comma-separated list. Round your answer four decimal places.) ln(3+x)=3
x= 17.0855
Let's solve the exponential equation 3e^x=45
x= 2.708
Use a calculator to find an approximation to the solution rounded to six decimal places 5^x=2^x+1
x= log base 5(2)/ 1- log base 5 (2) x= 0.756471
Use a calculator to find an approximation to the solution rounded to six decimal places. e^-7x=6
x=-0.255966
Solve the logarithmic equation for x. (Enter your answers as a comma-separated list log base 2 (x^2-4x-41)=2
x=-5,9
Find the solution of the exponential equation, as in Example 1 15^2x-3=1/15
x=1
Find the solution of the exponential equation, as in Example 1. (Enter your answers as a comma-separated list.) 2^2x-1=1
x=1/2
Use the definition of the logarithmic function to find x. (Simplify your answer completely.) log3(x) = −3 log base 3
x=1/27
ln(x)=-2 ln(1/e)=x
x=1/e^2 x=-1
Solve the logarithmic equation for x. (Enter your answers as a comma-separated list.) log(x-8)=4
x=10008
Let's solve the logarithmic equation log(3)+log(x-8)=log(x)
x=12
logx(5)=1/2 logx(3)=1/3
x=25 x=27
Solve for x. log base 5 (x-2)
x=27
Find the solution of the exponential equation, as in Example 1. (Enter your answers as a comma-separated list.) 4^x-1=16
x=3
Use the definition of the logarithmic function to find x. (Simplify your answer completely.) log5(625) = x log base 5
x=4
Find the solution of the exponential equation, as in Example 1 e^x^2=e^16
x=4,-4
Solve the logarithmic equation for x, as in Example 7. 2log(x)=log(2)+log(3x-4)
x=4,2
Solve the logarithmic equation for x, as in Example 7. (Enter your answers as a comma-separated list.) log(x)+log(x-2)=log(4x)
x=6
Solve the logarithmic equation for x, as in Example 7. (Enter your answers as a comma-separated list.) log base 3 (4)+ log base 3 (x)= log base 3 (6)+log base 3 (x-3)
x=9
e^x=9 e^2=y
x=log base e(9) 2=log base e(y)
2^x=30 5^7=w
x=log2(30) 7=log5(w)
Solve for y. (Enter an exact number.) y = ln(e^17)
y=17
