need help with a few math problemss?

Question

Q1 ..Solve the problem. Round your answer to three decimals.
What annual rate of interest compounded continuously is required to double an investment in 6 years?

Q2 ..The size P of a small herbivore population at time t (in years) obeys the function P(t) = 500e0.25t if they have enough food and the predator population stays constant. After how many years will the population reach 1000

Q3.. The Family Fine Arts Center charges $24 per adult and $10 per senior citizen for its performances. On a recent weekend evening when 478 people paid admission, the total receipts were $6992. How many who paid were senior citizens?

thankss alott .. i really am bad in mathh :(

Answer 1

(Q1) For interest compounded continuously, we need the equation

FV = Pe^Yr

where FV = future value, P = original investment, e is the base of the natural log, Y is the time in years, and r the annual interest rate.

You want to double your money in seven years, so solve

2P = Pe^( 7 r )
2 = e^ ( 7r )
ln ( 2 ) = 7r
ln ( 2 ) / 7 = r = .099

So interest of just a shade less than 10% per year will double your money in seven years.

(Q2) You are given the equation

P(t) = 500e^0.25t

and asked to find the time when P(t) is one thousand.

1000 = 500 e^.25t
2 = e^.25t
ln ( 2 ) = .25 t
ln ( 2 ) / .25 = t = 2.78 years

(Q3) Translating the words into equations where A = number of adults and C = number of senior citizens:

A + C = 478
24 A + 10 C = 6992

The first equation gives us A = 478 - C which we will then substitute into the second...

24 ( 478 - C ) + 10 C = 6992

11472 - 24 C + 10 C = 6992

4480 = 14 C

320 = C

So there were 320 senior citizens and 158 adults.

Checking: ( 24 ) ( 158 ) + ( 10 ) ( 320 ) = 6992 as expected.

Answer 2

1)okay, think about it, there is 1 kilogram for every 2.2 pounds so a kilogram is a little more than twice as big as a pound if something weighed 2 kg, it would obviously weight 4.4 lbs 3 kg would be 6.6 pounds (see the pattern, its multiplying by 2.2) the conversion is usually written this way: 50 kg * (2.2 lbs/kg)=110 lbs (a small person, get the idea?) the other passengers are of course figured the same way 2) once you know their weight in lbs, you are supposed to balance them for the ride, you can't put an even number on each side, so you have to have two on one side and three on the other clearly one or both of your big people are going to have to be on the two person side just try adding up different combinations (using the wieghts in lbs that you calculated in the first step) and when you have a group of 3 and a group of 2 that are within 25 lbs of each other, you are there 3) remember that a ton is 1000 lbs, and so half a ton is 500 lbs add up the weights of all the family (in the lbs from problem #1) and subtract that number from 500, and you can see how much weight is left unused of the 500 lbs (half ton) that can be passengers think it through keep at it good luck math is power