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A cell doubles every hour. If there are $2$ cells initially, how many cells will there be after $3$ hours?

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Exponential growth and decay: word problems

Full solution

Q. A cell doubles every hour. If there are

2

cells initially, how many cells will there be after

3

hours?

Identify Initial Number: Identify the initial number of cells and the rate at which they double. $\newline$ Initial number of cells $a$ = $2$ $\newline$ Doubling rate = every hour $\newline$ Total time $t$ = $3$ hours $\newline$ We need to calculate the number of cells after $3$ hours using the formula for exponential growth: $N = a \times 2^t$ , where $N$ is the final number of cells, $a$ is the initial number of cells, and $t$ is the time in hours.
Substitute Known Values: Substitute the known values into the exponential growth formula. $\newline$ Using the formula $N = a \times 2^t$ , we substitute $a = 2$ and $t = 3$ . $\newline$ $N = 2 \times 2^3$
Calculate Exponent: Calculate the exponent part of the formula. $\newline$ $2^3$ means $2$ multiplied by itself $3$ times. $\newline$ $2^3 = 2 \times 2 \times 2$ $\newline$ $2^3 = 8$
Multiply Initial Number: Multiply the initial number of cells by the result from the exponent calculation to find the final number of cells. $\newline$ $N = 2 \times 8$ $\newline$ $N = 16$

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