After the four-year period, Siân withdraws 40 000 AU buy a car. It is known that the car will depreciate at a The value of the car will be 2500 AUD after t years. Find the value of t.

Q: Kimi invests $4,000 at 3% interest compounded continuously. How much money will she have in 4years?

A: Given principal(p)=$4000Interest rate(r)=3%=0.03time(t)=4 yearssince the amount is compounded…

Q: Mary invests $3500 at 2.75% compounded continuously. How much money will be in the account after 6…

A: Given that Invested amount=$3500 Interest compounded continuously =2.75% Time=6 years To find  How…

Q: (a) A radioactive substance has a half-life of 20 years. If 8 mg of the substance remains afte 100…

A: We will use radioactive decay formula ..

Q: Kyle investes in an account earning 8% interest compound continuously. How long will it take to…

A:

Q: Kimi invests $4,000 at 3% interest compounded continuously. How much money will she have in4 years?

A:

Q: Tara placed $1200 in a savings account which compounds interest continuously at a rate of 1.4%. How…

A:

Q: Solve the equation for x. arctan(2x − 5) = −1

A: Given: arctan(2x − 5) = −1 To find: Solve the given equation for the value of x Calculation:…

Q: he amount of a certain radioactive substance decreases by 15% every hour. If a sample starts with…

A:

Q: Dash invested $10,000 at 3% interest compounded continuously. How much will he have after 8 years?

A: The formula for compound interest is, A = Pert A = Final Amount P = Principal r = rate of interest t…

Q: After one year, a sample of radioactive material disintegrates to 94% of the original amount. For…

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Q: A bacteria culture starts with 3000 bacteria and grows to 50,000 in 3 hours. a) What is the doubling…

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Q: Logan invests $4000 at an annual interest rate of 6%.How much money will she have after 10 years if…

A:

Q: Assume that a runner runs a 100 meter sprint in 12.3 seconds. He accelerates steadily in the first…

A: The runner accelerates steadily in the first 25 meters. Let the acceleration be a m/s2 and suppose…

Q: The count in a bateria culture was initially 300, and after 35 minutes the population had increased…

A: Given  Initially the count in a bacteria culture = 300 after 35 minutes the population had increased…

Q: A total of $50000 is invested, part of it at 5% and the rest at 7.5%. The totalinterest after one…

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Q: Hannah wants to have $6000 to help pay for a new deck in 10 years. If she wants to put her money…

A: Time has been valuable in all aspects but in terms of finance, time has a money value. The worth of…

Q: The half-life of radioactive cobalt is 5.27 years. Suppose that a nuclear accident has left the…

A: Given:    Half-life of radioactive cobalt =5.27 years    The proportion p that remains after y years…

Q: The rate of fingernail growth depends on many factors, but in adults, nails grow at an average rate…

A:

Q: At 10:30 am, detectives discover a dead body in a room and measure its temperature at 26◦C. One hour…

A: Recall the Newton's law of cooling. The differential equation satisfied by the body temperature,…

Q: The rate of fingernail growth depends on many factors, but in adults, nails grow at an average rate…

A: To determine the equation for the nails growth over the month

Q: After the release of radioactive material into the atmosphere from a nuclear power plant atChernobyl…

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Q: Bethany needs to borrow $8,000. She can borrow money at 6.9% simple interest for 3 yr or she can…

A:

Q: Find a formula for the exponential function passing through the points (-2,-) and (1,10) y =

A: On solving this we will asume firstly general exponential function so  we will get

Q: A certain radioactive substance has a half-life of 38 hours. Find how long it takes for 90% of the…

A: A certain radioactive substance has a half-life of 38 hours. t1/2 = 38 hrs  We know that every…

Q: Jerome wants to invest $25,000 as part of his retirement plan. He can invest the money at 5.2%…

A: Given:

Q: The half-life of carbon-14 is 5730 years. A frozen human mummy was discovered in a glacier. It was…

A:

Q: Lea invests $8,333 in a savings account with a fixed annual interest rate of 8%. What will the…

A: According to questionInitial balance (p) = $8,333Interest rate (r) = 8%Time (t) = 12 yearIt is given…

Q: The cost of installing insulation in a particular two-bedroom home is $2400. Present monthly heating…

A: The insulation costs for the two bedroom  home is $2400.The costs of monthly heating in present…

Q: A saving account deposit of $150 is to earn 6.5% compound continuously. To the nearest year how many…

A:

Q: The value of a CNC milling machine, originally valued at £240000, depreciates 15% per annum.…

A: Depreciation formula , P=Po(1-(r/100))n Where Po= original value P is the value after n years r=…

Q: At the beginning of an experiment, a scientist has 228 grams of radioactive goo. After 135 minutes,…

A: Given that: P=the initial amount= 228 Time=t=135 minutes A=final amount= 3.5625 r=rate    Using the…

Q: the amount of a given radioactive substance today is 8 grams. After 10 years, the amount remaining…

A:

Q: How long must $3700 be invested at 9% p.a. simple interest to give interest of $2331?

A: We will find out the required value.

Q: Teri invested $1500 in an account with an interest rate of 2.25% compounded continuously. How long…

A: Initial investment=$1500 Rate of interest=2.25% We need the time in which the earnings will be $5000

Q: Find the balance if P50 , 000 is invested at an annual rate of 10% for 5 years compounded…

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Q: How long, to the nearest year, will it take an investment to triple if it is continuously compounded…

A: Continuous compound interest formula: The amount in an account after t years at r rate is compounded…

Q: Kimi invests $4,000 at 3% interest compounded continuously. How much money will she have in 4 years?

A: Given that,   Invest value (P) =$4000   Interest rate(r) = 3%   Time (t) =4 years

Q: a hospital purchases a ventilador for $45,000 that has a useful life of 10years. The salvage value…

A: Given that: A hospital purchases a ventilator for $45,000 that has a useful life of 10years. The…

Q: The half-life of Fermium-253 is 3 days. If a sample initially contains 100 mg, how many milligrams…

A: Half-life Formula: Where,  N(t) = amount left after time t                N0 = Initial amount…

Q: Kyle invests in an account earning 7.75% interest compounded continuously. How long will it take to…

A:

Q: Solve for the arbitrary constant. Show complete solution. ln y = c1sin3x + c2cos3x + 9x2-2

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Q: The half-life of polonium is 139 days, but your sample will not be useful to you after 82% of the…

A:

Q: Suppose an Egyptian mummy is discovered in which the amount of carbon-14 present is only about…

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Q: After 25 years, your savings account has now grown to $16,200 and has an interest of 6.1% that…

A:

Q: Solve for: a² S(sec³0 – sec®)d0

A: To solve: a2∫sec3θ-secθdθ Solution: Evaluating the integral. I=a2∫sec3θ-secθdθ=a2∫sec3θ dθ-∫secθ dθ…

Q: James wants to invest $8,000. He can invest the money at 7.2% simple interest for 30 yr or he can…

A:

Q: A radioactive substance is decaying according to the formula y = Be-0.02t , where y mg is the amount…

A:

Q: The half-life of cesium-137 is 30 years. Suppose you have a 80 mg sample. After how long will only 1…

A:

Q: if $2000 is invested at 5%, compounded continuosly for t years, the value, A of the investment is…

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.