Questions: A group of cells grows in number as described by the equation y=16(2)^t, where t represents the number of days and y represents the number of cells. According to this formula, how many cells will be in the group at the end of the first 5 days? A. 80 B. 160 C. 400 D. 512 E. 1,280

A group of cells grows in number as described by the equation y=16(2)^t, where t represents the number of days and y represents the number of cells. According to this formula, how many cells will be in the group at the end of the first 5 days?
A. 80
B. 160
C. 400
D. 512
E. 1,280

Transcript text: 19. A group of cells grows in number as described by the equation $y=16(2)^{t}$, where $t$ represents the number of days and $y$ represents the number of cells. According to this formula, how many cells will be in the group at the end of the first 5 days? A. 80 B. 160 C. 400 D. 512 E. 1,280

Solution

Solution Steps

To find the number of cells at the end of the first 5 days, substitute $ t = 5 $ into the given equation $ y = 16(2)^t $. This will give the number of cells after 5 days.

Step 1: Substitute $ t $ into the Equation

To find the number of cells after 5 days, we substitute $ t = 5 $ into the equation $ y = 16(2)^t $: \[ y = 16(2)^5 \]

Step 2: Calculate $ 2^5 $

Next, we calculate $ 2^5 $: \[ 2^5 = 32 \]

Step 3: Multiply by 16

Now, we multiply the result by 16: \[ y = 16 \times 32 = 512 \]