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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

A. When comparing the "# of Bacteria" each hour, what is the number being-example-1

2 Answers

5 votes

Answer:

Part A: B

Part B: C

Part C: A

Part D: D

Explanation:

User Anatoliy R
by
6.1k points
4 votes

Answer:

Part a) The number is 8

Part b) The initial number of bacteria is 4

Part c)
y=4(8)^x

Part d)
y=100(8)^x

Explanation:

we know that

The equation of a exponential function is equal to


y=a(b)^x

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


(32)/(a)=8

solve for a


a=32/8=4\ bacteria

Part c) Write a rule for this table

we have


y=a(b)^x

we have


a=4\\b=8

substitute


y=4(8)^x

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


a=100


b=8 ---> the growth factor is the same

so


y=100(8)^x

User Sago
by
5.4k points