Question

in e labroretsy, the count of bacterie
in a certain experiment was increasing the rate of
25% per hour. Find the bacteria and take at the
end of 2 hours if the court was initally 5,00,00​

Answer 1

GIVEN :-

• a = count of bacteria at the end of 2 hours

• p = initial count of bacteria = 5,00,00

• r = rate = 2.5%

• n = number of hours = 2

TO FIND :-

• number of bacteria take at the end of 2 hours if the court was initially 5,00,00

SOLUTION :-

now as we know that ,

initial count of bacteria = 5,00,00

and it is increasing at the rate of 2.5% per hour

so , here 2.5% is the compound rate

so we use the formula of compound interest :-

$\implies \boxed{ \rm{ a = p \: (1 + \dfrac{r}{100}) ^{n} }}$

NOW PUTTING VALUES IN FORMULA :-

$\implies \rm{ \: 50000 \: ( 1 + \dfrac{2.5}{100}) ^{2} }$

$\implies \rm{ \: 50000 \: ( \dfrac{100 + 2.5}{100}) ^{2} }$

$\implies \rm{ \: 50000 \: ( \dfrac{102.5}{100}) \:( \dfrac{102.5}{100}) }$

$\implies \rm{ \: 5 \times 102.5 \times 102.5}$

$\implies \boxed { \boxed{\rm{ a \: = 52531.25}}}$

OTHER INFORMATION :-

Compound Interest Definition :

• Compound interest is the interest calculated on the principal and the interest accumulated over the previous period. It is different from the simple interest where interest is not added to the principal while calculating the interest during the next period.

• Compound interest finds its usage in most of the transactions in the banking and finance sectors and also in other areas as well.

Some of its applications are:

• Increase or decrease in population.

• The growth of bacteria.

• Rise or Depreciation in the value of an item.