Chapter 9, Problem 83SGR

To determine

To calculate: To find the number of bacteria in $1$ hours

Answer to Problem 83SGR

Number of bacteria in dish after $1$ hour is $4000$

Explanation of Solution

Given information: Starting from a single bacterium in a dish, the number of bacteria after $t$ cycles of reproduction is $2^t$ and a bacterium reproduces after $30$ minutes. Also there are $1000$ bacteria in a dish now

Formula Used:

Linear equations are the equations that do NOT have

• Exponents (like $2$ in $x^2$)
• Roots (like square roots, cube roots, etc)

Degree of the linear equation is always equal to $1$

Calculation:

Number of bacteria after $t$ cycles reproduction of one bacterium is given as

  $2^t$

Thus, number of bacteria after $t$ cycles of reproduction of $1000$ bacteria is calculated as

  $Rate=1000\times 2^t---(1)$

Also, bacteria reproduces in $30$ minutes and given time is $1$ hours

Thus, number of cycles in $1$ hours $=2$

Now, substituting the value of $t=2$ in equation (1),

  $\begin{array}{l}Number=1000\times 2^2\\ Number=1000\times 4\\ Number=4000\end{array}$

Conclusion:

Hence, number of bacteria in dish after $1$ hour is $4000$