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ira [324]
3 years ago
10

Please help, last two questions.

Mathematics
1 answer:
Novay_Z [31]3 years ago
5 0
First problem.
The function is f(x) = 3^x.
The base, b, is 3 since 3 is raised to power x.
The question is what value of x used in 3^x makes the expression 3^x equal to 3?
Look at the graph, and find the point that has y-value 3.
Which x-value does that point have?
The point is (1, 3), and the x-value is 1.

Second question.
The question is similar to the question above using a different exponential function.
(1/4)^1 = 1/4, so the answer is x = 1
You might be interested in
From 1990 to 2000, the population of Florida increased by 2.13% per year. The population (in millions) in the year 1990 was 16 E
belka [17]

Answer:

19 million

Step-by-step explanation:

So generally whenever we express a exponential function, it's in the form: y=a(b)^x

where a=initial value aka when x=0

in this case, b can be expressed as: 1+r, where r is the growth rate, which in this case is 2.13%, and expressing that as a decimal (divide by 100), r=0.0213, thus b=1.0213

This gives us the following equation: y=16(1.0213)^x

To kind of give you a intuitive reason as to why this makes sense, think of that 1.0213 wrapping around the previous value.

So when x=0, it's actually just 16, since any number (besides 0) to the power of 0, equals 1.

When x=1, we get: 1.0213(16), which can be expressed as a 2.13% increase from year 0

When x=2, we get: 1.0213(1.0213(16)), which can be expressed as a 2.13% increase from year 1

when x=3, we get: 1.0213(1.0213(1.0213(16))), which can be expressed as a 2.13% increase from year 2.

In other words, each year we're getting another 1.0213 to multiply by (very definition of an exponent).

So to calculate the population in 1997, we put in x=7, since it's 7 years after 1990

We get the following equation: y=16(1.0213)^7

Using a calculator this simplifies to approximately: 18.5436

Rounding this to the nearest integer would yield 19, and since the values are expressed in millions, the answer would be 19 million

4 0
1 year ago
Carlos went to gas station A and paid $54 for 25 gallons. Sasha went to gas
RideAnS [48]

Answer: Sasha

Step-by-step explanation:

carlos- 54 divided by 25 equals 2.25 dollars for each gallon

sasha- 31.25 divided by 15 equals 2.083333(3 repeats)

They are both really close on price, but sasha's is cheaper

5 0
2 years ago
Is there a relationship between the different of the integers and the distance between them?
user100 [1]

Wait just a minute.  Hold up.  Hee haw. Whoa !

Coming down to Earth for just a second ... what in the world is
the "distance" between integers anyway !
7 0
3 years ago
Read 2 more answers
Adam must fly home to city A from a business meeting in city B. One flight option flies directly to city A from​ B, a distance o
g100num [7]

Answer:

The value  is  k =109.6 \ miles

Step-by-step explanation:

The diagram illustrating the question is shown on the first uploaded image

From the question we are told that

   The distance from city A to B is   AB =  467.3 miles

   The bearing from B to  C is  \theta_{BC} =  N 28.7E

   The bearing from B to  A is  \theta_{BA} =  N 60.7E

   The  bearing from A to  B is   \theta_{AB} =  S60.7W

    The  bearing from A to  C is   \theta_{AC} =  S79.1W

Generally from the diagram

     \theta_A  =  180 - 60.7 -79.1

=>  \theta_A  =  40.2 ^o

Also

     \theta_B  =  32^o

and  

      \theta_C  =  180 - (\theta_A  +\theta_B )

=>   \theta_C  =  180 - (40.2  + 32 )

=>   \theta_C  =  107.8 ^o

Generally according to Sine Rule

     \frac{BC}{sin (\theta_A)}  = \frac{CA}{sin (\theta_B)} =\frac{AB}{sin (\theta_C)}

=>   \frac{BC}{sin (40.2)}  = \frac{CA}{sin (32)} =\frac{467.3 }{sin (107.8)}    

So

     \frac{BC}{sin (40.2)}  = \frac{467.3 }{sin (107.8)}

=>  BC = 316.8 \ miles

Also  

    \frac{CA}{sin (32)} =  \frac{467.3 }{sin (107.8)}

    CA = 260 .1 \ miles

Generally the additional flyer miles that Adam will receive if he takes the connecting flight rather than the direct​ flight is mathematically represented as

      k = [CA +BC]  - AB

=>     k = [260 .1 +316.8]- 467.3

=>  k =109.6 \ miles

4 0
3 years ago
The machinist's goal was to increase his production by at least 10% each day. Assume he achieved his goal. If he was able to mac
quester [9]
25+10%= 27.5 Hope this helps.
8 0
3 years ago
Read 2 more answers
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