What is the slope of the line that passes through the points e(-1,4) and f(2,6)?
1 answer:
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Answer:
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
Answer:
4 19/20 hours or 4 hours , 57 minutes
Step-by-step explanation:
Given
In 9 hours Maria can fill a certain order let Say X
In 9/9 hours Maria can fill X/9 of the order
in 1 hour Maria can fill X/9 of the order
__________________________________
In 11 hours Jim can fill a certain order let Say X
In 11/11 hours Maria can fill X/11 of the order
in 1 hour Maria can fill X/11 of the order
_____________________________________________
Therefore total order filled by them in one hour will sum of individual work done by them in one hour.
Mathematically,
total order filled by Jim and maria in one hour = work done by Jim in one + work done by Maria in one hour
total order filled by Jim and maria in one hour = 1/11 + 1/9
=>
=>20/99 of certain order is filled by both of them in one hour.
=>Total order is one. Hence, to get 1 from 20/99 we need to multiply it with its reciprocal (i.e 99/20) as 20/99 *99/20 = 1
now
=>20/99 of certain order is filled by both of them in 1 hour.
=>multiplying both order and hour with 99/20 we have
20/99 *99/20 of certain order is filled by both of them in 1* 99/20 hour
Thus total order is filled by them in 99/20 hours = 4 19/20 hours.
1 hour has 60 minutes
so 19/20 has 60*19/20 minutes = 57 minutes.
Working together, Jim and Maria will take 4 hours , 57 minutes to fill the order.