Advertisements
Advertisements
Question
The count of bacteria in a culture grows by 10% in the first hour, decreases by 8% in the second hour and again increases by 12% in the third hour. If the count of bacteria in the sample is 13125000, what will be the count of bacteria after 3 hours?
Advertisements
Solution
\[Given: \]
\[ R_1 = 10 % \]
\[ R_2 = - 8 % \]
\[ R_3 = 12 % \]
P = Original count of bacteria = 13, 125, 000
We know that:
\[P\left( 1 + \frac{R_1}{100} \right)\left( 1 - \frac{R_2}{100} \right)\left( 1 + \frac{R_3}{100} \right)\]
∴ Bacteria count after three hours \[= 13, 125, 000\left( 1 + \frac{10}{100} \right)\left( 1 - \frac{8}{100} \right)\left( 1 + \frac{12}{100} \right)\]
\[ = 13, 125, 000\left( 1 . 10 \right)\left( 0 . 92 \right)\left( 1 . 12 \right)\]
\[ = 14, 876, 400\]
Thus, the bacteria count after three hours will be 14, 876, 400.
APPEARS IN
RELATED QUESTIONS
Find the compound interest on Rs 160000 for one year at the rate of 20% per annum, if the interest is compounded quarterly.
Compute the amount and the compound interest in the following by using the formulae when:
Principal = Rs 2000, Rate = 4 paise per rupee per annum, Time = 3 years
Compute the amount and the compound interest in the following by using the formulae when:
Principal = Rs 160000, Rate = 10 paise per rupee per annum compounded half-yearly, Time = 2 years.
There is a continuous growth in population of a village at the rate of 5% per annum. If its present population is 9261, what it was 3 years ago?
In a factory the production of scooters rose to 46305 from 40000 in 3 years. Find the annual rate of growth of the production of scooters.
The annual rate of growth in population of a certain city is 8%. If its present population is 196830, what it was 3 years ago?
The population of a town increases at the rate of 50 per thousand. Its population after 2 years will be 22050. Find its present population.
Ashish started the business with an initial investment of Rs 500000. In the first year he incurred a loss of 4%. However during the second year he earned a profit of 5% which in third year rose to 10%. Calculate the net profit for the entire period of 3 years.
Sameerrao has taken a loan of ₹ 12500 at a rate of 12 p.c.p.a. for 3 years. If the interest is compounded annually, then how many rupees should he pay to clear his loan?
The population of a town was decreasing every year due to migration, poverty and unemployment. The present population of the town is 6,31,680. Last year the migration was 4% and the year before last, it was 6%. What was the population two years ago?
