A. When comparing the "# of Bacteria" each hour, what is the number being multiplied by each time? *
1
8
32
224
b. What is the initial number of bacteria? (at time zero) *
0
1
4
32
c. Write a rule for this table. *
y = 4 * 8^x
y = 4 + 8x
y = 4^x + 8
y = 4x + 8
d. Suppose you started with 100 bacteria, but they still grew by the same growth factor. Write the function rule for this situation. *
y = 4 * 100^x
y = 100x + 8
y = 100x + 4
y = 100 * 8^x

Part a) The number is 8

Part b) The initial number of bacteria is 4

Part c)

Part d)

Step-by-step explanation:

we know that

The equation of a exponential function is equal to

where

y is the number of bacteria

x is the time in hours

b is the base of the exponential function

a is the initial number of bacteria

Part a) When comparing the "# of Bacteria" each hour, what is the number being multiplied by each time?

we know that

For x=1 h ----> y=32 bacteria

For x=2 h ----> y=256 bacteria

For x=3 h ----> y=2,048 bacteria

For x=4 h ----> y=16,384 bacteria

For x=5 h ----> y=131,072 bacteria

For x=6 h ----> y=1,048,576 bacteria

so

256/32=8

2,048/256=8

16,384\2,048=8

131,072/16,384=8

1,048,576\131,072=8

so

the base of the exponential function  b is 8

Part b) What is the initial number of bacteria? (at time zero)

we know that

The number of bacteria at time x=1 hour , divided by the number of bacteria at time x=0 must be equal to 8 (see part a)

so

solve for a

Part c) Write a rule for this table

we have

we have

substitute

Part d) Suppose you started with 100 bacteria, but they still grew by the same growth factor. Write the function rule for this situation

In this case

---> the growth factor is the same

so