Full solution

Q. A mold culture covering

125 \mathrm{~cm}^{2}

shrinks to two-fifths of the previous day's size each day. How big is mold culture after five days?

Understand the problem: Understand the problem. $\newline$ We are given that a mold culture starts at $125 \, \text{cm}^2$ and shrinks to two-fifths of its size each day. We need to find out the size of the mold culture after five days.
Determine formula: Determine the formula to calculate the size of the mold culture after each day. $\newline$ The size of the mold culture after each day can be calculated by multiplying the current size by two-fifths $\frac{2}{5}$ .
Calculate day $1$ : Calculate the size of the mold culture after the first day. $\newline$ Size after day $1$ = Initial size $\times$ $\frac{2}{5}$ $\newline$ Size after day $1$ = $125 \, \text{cm}^2$ $\times$ $\frac{2}{5}$ $\newline$ Size after day $1$ = $50 \, \text{cm}^2$
Calculate day $2$ : Calculate the size of the mold culture after the second day. $\newline$ Size after day $2$ = Size after day $1$ $\times$ $\frac{2}{5}$ $\newline$ Size after day $2$ = $50 \, \text{cm}^2$ $\times$ $\frac{2}{5}$ $\newline$ Size after day $2$ = $20 \, \text{cm}^2$
Calculate day $3$ : Calculate the size of the mold culture after the third day. $\newline$ Size after day $3$ = Size after day $2$ $\times$ $\frac{2}{5}$ $\newline$ Size after day $3$ = $20 \, \text{cm}^2$ $\times$ $\frac{2}{5}$ $\newline$ Size after day $3$ = $8 \, \text{cm}^2$
Calculate day $4$ : Calculate the size of the mold culture after the fourth day. $\newline$ Size after day $4$ = Size after day $3$ $\times$ $\frac{2}{5}$ $\newline$ Size after day $4$ = $8 \, \text{cm}^2$ $\times$ $\frac{2}{5}$ $\newline$ Size after day $4$ = $3.2 \, \text{cm}^2$
Calculate day $5$ : Calculate the size of the mold culture after the fifth day. $\newline$ Size after day $5$ = Size after day $4$ $\times$ $\frac{2}{5}$ $\newline$ Size after day $5$ = $3.2$ cm $^2$ $\times$ $\frac{2}{5}$ $\newline$ Size after day $5$ = $1.28$ cm $^2$