By what percent will a fraction decrease if its numerator is increased by 20% and its denominator is increased by 50%?

Mathematics

2 answers:

ss7ja [257]2 years ago

7 0

Answer: 20%

Step-by-step explanation:

Lets call one number x and the other one y

first you have the fraction x/y

When you increase the numerator by 20% you get 1.2

when you increase the denominator by 50% you get 1.5

Then you get the fraction 1.2x/1.5y

since fractions are basically division you divide 1.2 by 1.5 which is 0.8

0.8 as a percent is 80%

you subtract that from 100 and you get 20%

Brums [2.3K]2 years ago

3 0

Lets find out...

our fraction is 1/2.....
when the numerator is increased by 20%......1 + 0.20(1) = 1.2
when the denominator is increased by 50%....2 + 0.50(2) = 3

1/2 = 0.5....original fraction
1.2 / 3 = 0.4.....increased fraction

decrease = (original number - new number) / original number...* 100
= (0.5 - 0.4) / 0.5...* 100
= (0.1 / 0.5)....* 100
= 0.2 * 100
= 20% decrease <====

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A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has i

goldfiish [28.3K]

Answer:

P(t) = 100·2.3^t
529 after 2 hours
441 per hour, rate of growth at 2 hours
5.5 hours to reach 10,000

Step-by-step explanation:

It often works well to write an exponential expression as ...

value = (initial value)×(growth factor)^(t/(growth period))

(a) Here, the growth factor for the bacteria is given as 230/100 = 2.3 in a period of 1 hour. The initial number is 100, so we can write the pupulation function as ...

P(t) = 100·2.3^t

(b) P(2) = 100·2.3^2 = 529 . . . number after 2 hours

(c) P'(t) = ln(2.3)P(t) ≈ 83.2909·2.3^t

P'(2) = 83.2909·2.3^2 ≈ 441 . . . bacteria per hour

(d) We want to find t such that ...

P(t) = 10000

100·2.3^t = 10000 . . . substitute for P(t)

2.3^t = 100 . . . . . . . . divide by 100

t·log(2.3) = log(100)

t = 2/log(2.3) ≈ 5.5 . . . hours until the population reaches 10,000