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Ilya [14]
3 years ago
5

Does the table represent a exponential function x 1 2 3 4 y -1 -8 -27 -64

Mathematics
1 answer:
Setler79 [48]3 years ago
8 0

Answer:

No, the given function is not an exponential function.

Step-by-step explanation:

The exponential function is defined as

f(x)=ab^x                   .... (1)

Where a is initial value and b is growth factor.

From the given table it is noticed that the value of y decreased as the value of x increased by 1. The function is in the form of

f(x)=-x^3                  .... (2)

f(1)=-(1)^3=-1

f(2)=-(2)^3=-8

f(3)=-(3)^3=-27

f(4)=-(4)^3=-64

The function (1) and (2) are not the same type of function.

The table represents the polynomial.

Therefore the required answer is no. The given function is not an exponential function.

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Answer:

A) 63.36 years.

B) 100.42 years.

Step-by-step explanation:

We have been given that the population of the world was 7.1 billion in 2013, and the observed relative growth rate was 1.1% per year.

A) Since we know that population increases exponentially, therefore we will use our given information to form an exponential model for population increase and then we will solve for the time by which our population will be double.

P(t)=7.1(1.011)^{t}            

7.1 \times 2=7.1(1.011)^{t}  

\frac{7.1 \times 2}{7.1} =(1.011)^{t}

2 =(1.011)^{t}

Now let us solve for t using logarithm.

ln(2) =ln (1.011)^{t}      

ln(2) =t \cdot ln(1.011)

0.6931471805599453 =t \cdot 0.0109399400383344  

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t=63.3593217267282743049\approx 63.36

Therefore, it will take 63.36 years the population to be double.

B) Now we will find the number of years it will take the population to be triple of its size.

7.1 \times 3=7.1(1.011)^{t}

\frac{7.1 \times 3}{7.1} =(1.011)^{t}  

3 =(1.011)^{t}

Now let us solve for t using logarithm.        

ln(3) =ln (1.011)^{t}

ln(3) =t \cdot ln(1.011)

1.0986122886681097 =t \cdot 0.0109399400383344  

t=\frac{1.0986122886681097}{0.0109399400383344}

t=100.4221490079915311298\approx 100.42

Therefore, it will take 100.42 years the population to triple of its size.


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