A 1000 gallon tank, initially full of water, develops a leak at the bottom. Given that 200 gallons of water leak out in the first 10 minutes, find the amount of water, A(t), left in the tank t minutes after the leak develops if the water drains off at a rate proportional to the amount of water present. a) A(t) = 1000 (4/5)^-1/10 t b) A(t) = 1000 e^1/10 t c) A(t) = 1000 (2/3)^1/10 t d) A(t) = 1000 (1004/5)^t e) A(t) = 1000 e^-1/10 t f) None of the above.

ege

step-by-step explanation:

egge

b

step-by-step explanation:

it have 5 sides and 5 identicle angle.the rest does not have the same property as b.

brainliest

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt

answer: (3,11) is your answer.