Question

State whether the statement is True (T) or False (F).

To calculate the growth of a bacteria if the rate of growth is known, the formula for calculation of amount in compound interest can be used.

• A. True
• B. False

Answer 1

The correct option is A True

Explanation:

Compound interest is the interest calculated on the principal and the interest accumulated over the previous period. The compound interest formula is given below:

Compound Interest = Amount – Principal

Here, the amount is given by,

$A=P\times {\left(1+\frac{R}{100}\right)}^{nt}$, where,

• $\mathrm{A}$ = amount
• $\mathrm{P}$ = principal
• $\mathrm{R}$ = rate of interest
• $\mathrm{n}$ = number of times interest is compounded per year
• $\mathrm{t}$ = time (in years)

Let $P$ be the number of bacteria at the beginning of a certain year. If the constant rate of growth in the growth of bacteria is $R\%$ per annum, then the bacteria growth is also compounded it means the growth of bacteria depends on the number of bacteria last year same like in compound interest.

Thus, The number of bacteria after n years $=P\times {\left(1+\frac{R}{100}\right)}^n$

Therefore, the formula for calculating bacterial growth and the formula for calculating compound interest are the same.

Hence, the given statement is true.