Question

A. When comparing the "# of Bacteria" each hour, what is the number being multiplied by each time? *

Answer 1

Answer:

Part a) The number is 8

Part b) The initial number of bacteria is 4

Part c) $y=4(8)^x$

Part d) $y=100(8)^x$

Step-by-step 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

$\frac{32}{a}=8$

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

$y=100(8)^x$

Answer 2

Answer:

Part A: B

Part B: C

Part C: A

Part D: D

Step-by-step explanation: