The number of bacteria in a certain culture doubles every hour.

Solution:

To find: The number of bacteria after

(i) $2^{\text {nd }}$ hour

(ii) $5^{\text {th }}$ hour

(iii) nth hour

Given: (i) Initially, there were 50 bacteria

(ii) Rate – 100% per hour

The formula used: $A=P\left(1+\frac{r}{100}\right)^{t}$

(i) For $2^{\text {nd }}$ hour

$\Rightarrow$ No. of bacteria $=50\left(1+\frac{100}{100}\right)^{2}$

$\Rightarrow$ No. of bacteria $=50(1+1)^{2}$

$\Rightarrow$ No. of bacteria $=50(2)^{2}$

$\Rightarrow$ No. of bacteria $=50 \times 4$

$\Rightarrow$ No. of bacteria $=200$

(ii) For $5^{\text {th }}$ hour

$\Rightarrow$ No. of bacteria $=50\left(1+\frac{100}{100}\right)^{5}$

$\Rightarrow$ No. of bacteria $=50(1+1)^{5}$

$\Rightarrow$ No. of bacteria $=50(2)^{5}$

$\Rightarrow$ No. of bacteria $=50 \times 32$

$\Rightarrow$ No. of bacteria $=1600$

(iii) For $\mathrm{n}^{\text {th }}$ hour

$\Rightarrow$ No. of bacteria $=50\left(1+\frac{100}{100}\right)^{n}$

$\Rightarrow$ No. of bacteria $=50(1+1)^{n}$

$\Rightarrow$ No. of bacteria $=50(2)^{\mathrm{n}}$

$\Rightarrow$ No. of bacteria $=2^{n} 50$

Ans) Number of bacteria in a $2^{\text {nd }}$ hour will be 200 , the number of bacteria in a $5^{\text {th }}$ hour will be 1600 and number of bacteria in an $\mathrm{n}^{\text {th }}$ hour will be $2^{n} 50$