Question 572025: Please help! In the following, write an expression in terms of the given variables that represents the indicated quantity:
d. The amount of bacteria after n min if the initial amount of bacteria is q and the amount of bacteria triples every 30 seconds. (Hint: The answer should contain q as well as n.)
e. The temperature t hour ago if the present temperature is 40F and each hour it drops by 3F.
f. Pawel’s total earnings after three years if the first year his salary was s dollars, the second year it was $5,000 higher, and the third year it was twice as much as the first year.
g. The sum of three consecutive even whole numbers if the greatest is x.
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! d. The amount of bacteria after n min if the initial amount of bacteria is q and the amount of bacteria triples every 30 seconds. (Hint: The answer should contain q as well as n.)
The time, n, is in minutues, so the amount triples every 1/2 min.
After the 1st 1/2 min., the amount
The expression will be of the form q(n) = q*3^(kn)
We need to find the coefficient, k:
After 1/2 min. the amount will be 3q, which means (1/2)k = 1 -> k = 2
So the equation is q(n)=q*3^(2n)
e. The temperature t hour ago if the present temperature is 40F and each hour it drops by 3F.
Let T(t) = the temperature t hours ago
If the temperature drops 3F every hour, and if the current temp. is 40, then:
the temp. 1 hr ago was 43, the temp. 2 hrs ago was 46, etc.
The equation that describes this is T(t) = 40 + 3t
f. Pawel’s total earnings after three years if the first year his salary was s dollars, the second year it was $5,000 higher, and the third year it was twice as much as the first year.
The total earnings will be s + s + 5000 + 2s = 4s + 5000
g. The sum of three consecutive even whole numbers if the greatest is x.
If the largest number is x, then the other two numbers are x-2 and x-4
So the sum = x + x-2 + x-4 = 3x-6
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