Answer:
a) The number of ants in week three is shown through the following geometric progression: 500*1.1*1.1*1.1
b) 1.21
Step-by-step explanation:
We know that 500 ants are increasing at a rate of 10% every week which means that we can calculate the week one ants like this
500*1.1
Week two
500*1.1*1.1
and so on.
We write the following equation
500(1.1)^n where n is the number of weeks
We plug in 8 and then 6 for n in the equation above and get
500(1.1)^8=1071.79
500(1.1)^6=885.78
Divide and get that p=1.21
This will be solved by solving for x first. Firstly you multiply the top equation by 2 and the bottom by -3. This will change both equation to (top)-10x+6y=-54 and (bottom) 27x-6y=-57. Now when you add the factors the y-values cancel out leaving you with; 17x=-3. now you have to divide by 17 on both sides giving you x=-0.17647058823 (not the prettiest solution but you can round if you want to). After that pick an equation to solve for y (I'm picking the top); the equation will be 5(-0.17647058823)+3y=-27. multiply the negative decimal and 5 to get -0.88235294117 (again not the prettiest). Add that to both sides which will give you 3y=-26.1176470588. After this divide both sides by 3 which will give you y=-8.70588235294. Your answer is (-0.17647058823,-8.70588235294) You can divide to the second or third decimal if needed-----remember that as you round from left to right on a decimal if it's below five you leave it and if it's above 5 then round up 1. I hope this help :)
(3,15)(6,30)
slope = (30 - 15) / (6 - 3) = 15/3 = 5...so 5 gallons wasted per day
3^4 means 3 to the 4th power.
This means that you would multiply 3 by itself 4 times
It would look like this...3*3*3*3
3^4=81
