Logarithmic Equations

Information For questions 1 - 6, solve each logarithmic equation. Then, check all potential solutions. You must show all work for full credit. Question 1 In x - In 3 = In 4 Not yet answered X = Points out of 16.67 Question 2 2 . log4x - log(x - 1) = 1 Not yet answered X = Points out of 16.67Question 3 log(16+2b) = log(62-46) Not yet answered . List your answers from lowest to highest. Points out of 16.67 b = and b = Question 4 7In (5x -3) = 28 Not yet answered Points out of Ff VC 16.66Question 5 log3 (2x) - 1093(x-3) =1 Not yet answered X = Points out of 16.66 Question 6 log Ax+ log, (x - 12) = 3 Not yet answered . Be sure to provide any extraneous solutions. Points out of 16.67 Ff VCInformation For questions 1 - 2, the logistic function below models the number of students who have heard a rumor at Ridgeview High School. f(x ) = 2000 1+ 399ex Question 1 What is the carrying capacity of the function? Not yet answered Select one: Points out of O a. 2000 12.50 O b. 50 O c. 399 O d. 500 Question 2 What is the initial number of students who heard the rumor? Not yet answered Select one: Points out of O a. 5 12.50 O b. 40 O c. 20 O d. 10Information 25 For questions 3 - 4, use the logistic function: f(x) = 1+4 .0.2x Question 3 What is the carrying capacity of the function? Not yet answered Select one: Points out of O a. 4 12.50 O b. 5 O c. 1 O d. 25 Question 4 What is the y-intercept of the function? Not yet answered Select one: Points out of O a. 1 12.50 O b. 25 O c. 4 O d. 5Question 5 C A logistic function has a carry capacity of 100,000. Use the formula f(x) = - Not yet 1 + a . b x to write the logistic function if the points (0, answered 200) and (3, 800) are also on the function. Points out of 12.50 Select one: O a. f ( x ) = 100,000 1+499 . (0.3713)* O b. f( x ) = 100,000 1+499 . (0.6287)* OC. f ( x ) = 100,000 1-499 . (0.6287)* o d. f( x ) = 100,000 1-499 . (0.3713)*Information For questions 6 - 8, use the scenario below. Then, fill in the blanks to make true statements. The number of students infected with flu after x days at a local community college is modeled by the logistic function N( x ) = - 3500 1 + a . 6 * y . There are initially 25 students infected by flu. After 4 days, 450 students have the flu. Question 6 The value of a is Not yet answered Select one: Points out of O a. 149 12.50 O b. 99 O c. 139 O d. 150 Question 7 Find the value of b. The value of b is Not yet answered Select one: Points out of O a. 0.2578 12.50 O b. 0.5199 O c. 0.4699 O d. 0.4375 EQuestion 8 After 6 days, students are infected by flu. Round to the nearest whole. Not yet answered Select one: Points out of O a. 1451 12.50 O b. 1430 O c. 1402 O d. 1500Information For questions 1 - 10, use the formula A = P(1 + rt) to answer each question related to simple interest. Round all dollar amounts to the nearest cent. Round all interest rates to the nearest tenth. Question 1 Hayward invests $3000 in an account earning 4.5% simple interest. How much will he have after 8 years? Not yet answered Select one: Points out of O a. $4500.00 10.00 O b. $4100.00 O c. $4080.00 O d. $4250.00 O e. $4075.00 Question 2 Henry invests $2000 for 6 years at 3.75% simple interest. What is the total amount in the account after 6 years? Not yet answered Select one: Points out of O a. $2450.00 10.00 O b. $2500.00 O c. $2525.00 O d. $2425.00 O e. $2475.00Question 3 Hilda invests $10,000 at 5% simple interest. How much interest will she earn in 10 years? Not yet answered Select one: Points out of O a. $5250.00 10.00 O b. $5000.00 O c. $5500.00 O d. $5275.00 O e. $5565.00 Question 4 Harrison is 21 years old. He has $2300 to invest and plans to leave the money in an account until he is 70 years old. How much Not yet interest will Harrison earn at 3% simple interest? answered Points out of Select one: 10.00 O a. $3350.00 O b. $3375.00 O c. $3325.00 O d. $3380.00 O e. $3381.00Question 5 Holly has $2000 and needs to grow the money to $5000. How long will it take her to get the money if her interest rate is 3%? Not yet answered Select one: Points out of O a. 50 years 10.00 O b. 32 years O c. 25 years O d. 55 years O e. 51 yearsQuestion 6 Hannah plans to buy a $12,000 car for her daughter's 16th birthday. She plans to invest money for 8 years at 10% simple interest. Not yet What amount does she have to invest now to reach her goal? answered Points out of Select one: 10.00 O a. $6600.00 O b. $6333.33 O c. $6500.00 O d. $6666.67 O e. $6550.00 Question 7 Harley has $3000 to invest. He wants to have $35,000 in 25 years. What is Harley's interest rate? Not yet answered Select one: Points out of O a. 42% 10.00 O b. 42.7% O c. 45% O d. 42.5% O e. 43%Question 8 What starting balance grows to $9500 in 4 years with 6.5% simple interest? Not yet answered Select one: Points out of O a. $7525.00 10.00 O b. $7500.00 O c. $7450.00 O d. $7539.68 O e. $7649.82 Question 9 Harvey invests $4000 that he wants to grow to $8000 in 15 years. What simple interest will he need? Not yet answered Select one: Points out of O a. 6.33% 10.00 O b. 6.25% O c. 6.67% O d. 7% O e. 6.5%Question 10 Halston invests $4000 which earns 5% simple interest for the first 12 years and then 8% simple interest for the next 8 years. How Not yet much money will have he after 20 years? answered Points out of Select one: 10.00 O a. $10,496.00 O b. $15,598.00 O c. $15,795.00 O d. $16,800.00 O e. $16,825.00Quesmn 1 For questions 1 8, use the formula A = P(1 +i)t to find the value missing from each row. Round all dollar amounts to the nearest NOW\" cent. Round all interest rates and years to the nearest hundredth. answered Points out of 66.60 1. $1 ,000 7 1 .5% 2. $1,575 $2,250 5 |:| 3. $4,500 $5,534.43 3% 4. $10,000 12 2% 5. $1,670 $3,490 10 6. $17,000 $40,000 25 7. $10,000 $17,958.56 5% 8. $50,000 30 8% $1109.84 12 years 3.48% $4968.87 7.65% $7884.93 7 years 7.39% Question 2 Use the rule of 72 to estimate how long it takes money to double at 3% compound interest. Not yet answered Select one: Points out of O a. 9 years 8.35 O b. 12 years O c. 24 years O d. 8 years Question 3 Iris has $5000 to invest for 10 years. How much more money would she have if she earned 4% compound interest versus 4% Not yet simple interest? answered Points out of Select one: 8.35 O a. $450.00 O b. $425.33 O c. $401.22 O d. $478.13 O e. $435.76Question 4 Isabella invests $4000, which earns 5% compound interest for the first 12 years and then 8% compound interest for the next 8 Not yet years. How much money will she have after 20 years? answered Points out of Select one: 8.35 O a. $13,700.00 O b. $13,296.02 O c. $14, 195.03 O d. $13,250.00 O e. $14,256.07 Question 5 Ivan invests $10,000 at 2% compound interest for the first 8 years and then 5% compound interest for the next 7 years. How Not yet much money will he have after 15 years? answered Points out of Select one: 8.35 O a. $16,592.67 O b. $16,486.42 O c. $16,349.78 O d. $16,287.39 O e. $16, 193.54