Answer:
A(t) = amount remaining in t years
= A0ekt, where A0 is the initial amount and k is a constant to be determined.
Since A(1690) = (1/2)A0 and A0 = 80,
we have 40 = 80e1690k
1/2 = e1690k
ln(1/2) = 1690k
k = -0.0004
So, A(t) = 80e-0.0004t
Therefore, A(430) = 80e-0.0004(430)
= 80e-0.172
≈ 67.4 g
Step-by-step explanation:
Answer:
Volume = 113.1 cubic cm
Step-by-step explanation:
Complete the square fr x and y's sepreatly to get into form
(x-h)²+(y-k)²=r²
the center is (h,k) and radius is r
so
group x's and y's seperatly
(4x²-10x)+(4y²+24y)+133/4=0
undistribute leading confident from each
4(x²-2.5x)+4(y²+6y)+133/4=0
take 1/2 of each linear confident and square it and add negative and positive inside the parenthasees
-2.5/2=-1.25 (-1.25)²=1.5625
6/2=3, 3²=9
4(x²-2.5x+1.5625-1.5625)+4(y²+6y+9-9)+133/4=0
factor perfect squares
4((x-1.25)²-1.5625)+4((y+3)²-9)+133/4=0
expand
4(x-1.25)²-6.25+4(y+3)²-36+133/4=0
4(x-1.25)²+4(y+3)²-9=0
add 9 to both sides
4(x-1.25)²+4(y+3)²=9
divide both sides by 4
(x-1.25)²+(y+3)²=9/4
(x-1.25)²+(y+3)²=(3/2)²
the center is (1.25,-3) and the radius is 1.5
Answer:
< TRS and <VRW
Step-by-step explanation:
All you have to do is plug in the given x values. your first equations would read:
f(-3) = 2^(-3)
f(-2) = 2^(-2)
f(-1) = 2^(-1)
these can be solved by moving decimal points or entering them into a calculator. regardless of the method, your answers are:
f(-3) = 0.002
f(-2) = 0.02
f(-1) = 0.2
so just repeat that process to fill in the rest of your table. to graph it, you'll use them as normal (x, y) points:
(-3, 0.002)
(-2, 0.02)
(-1, 0.2)
the graph might be a little difficult, working with such small values, but precision isn't totally important--0.002 will be super close to 0, 0.02 will be slightly further, 0.2 will be slightly further. the smaller values don't matter as much graphically and you'll recognize the graph of a growing exponential as you graph more of the table.
