Exponential Functions Lab Solutions

Question 1

Similarities:

• Range is infinite with the exception of horizontal lines
• Domain is infinite
• both have y-intercepts
• can both be transformed
• both can be used to model real life situations

Differences:

• linear function has common difference ,exponential has common ratio
• linear function has constant slope
• we need the use of a tangent line when finding the slope of a exponential graph

Question 2

The y-intercept is at 3 because of you let x=0 you will get a answer of 3. The growth factor is 4.

Question 3

The value of a is 6,because anything with the base of 1 is just itself.

Question 4

It means that a is less than 1 because the graph is decreasing.

Question 5

f(x)=2*5^x

The 2 signifies the y-intercept and the 5 is the growth factor.

Question 6

It is equivalent to 16 fold because in one growth period it doubles, so growth periods it would double 4 times or in other words 2^4 which is equal to 16.

Group: Graeme, Mark, Ethan (I'm apologizing if i misspelled someone's name)

Exponential Functions Lab: Team Sandy/Robert/Aichelle

Hello,
Our group consisted of Sandy, Robert and me, Aichelle.

For question one, we came up with:
similar---> both have inverses.
different---> linear functions have a common difference; exponential functions have a common ratio.

For question two, we said the y-int. was 3 and the growth factor was 4.

We found the value of a to be six in question three.
We know this because:
we were given: f(x) = a ^ x and f(1)=6
so that means a ^ x = 6
and if x = 1
then, a ^ x = a ^ 1
a ^ 1 = 6
or
a ^ 1= 6 ^ 1
since they have the same exponent [1] we can say a = 6.

We said the graph is less than one because the graph is decreasing. As the x-value increases, the y-value decreases. Therefore, a has to be less than 1 in order for that to occur.

For question five we came up with an equation of f(x) = 2 * 5 ^ x.

And lastly, for question 6, we said that the salmonella bacteria growth that doubles every six hours is equivalent to a sixteen fold increase each day because:
there are 24 hours in a day and it takes 6 hours for the bacteria to double.
24hrs/6 hrs = 4 times the bacteria doubles in a day.
since it is doubling we must square how many times in doubles in a day.
4² = 16 times or 16 folds in a day.

Thanks...
---Sandy/Robert/Aichelle.