Determine whether each table or rule represents a linear or an exponential funct

Question

Determine whether each table or rule represents a linear or an exponential function. 3. y = 5 middot 2^x 4. y = 6 middot x^3 5. y = 3x - 8 6. y = 4 middot 0.3^x Evaluate each function for the given value. 7. f(x) = 5^x for x = 4 8. h(t) = 3 middot 4^t for t = -3 9. y = 8 middot 0.7^x for x = 3 Graph each exponential function. 10. f(x) = 3^x 11. y = 0.25^x 12. y = 8 middot 1.2^x 13. What is the solution or solutions of 3^x = 5x? 14. An investment of $8000 in a certain Certificate of Deposit (CD) doubles in value every seven years. The function that models the growth of this investment is f(x) = 8000 middot 2^x, where x is the number of doubling periods. If the investor does not withdraw any money from this CD, how much will be available for withdrawal after 28 years? 15. A population of amoebas in a petri dish will triple in size every 20 minutes. At the start of an experiment the population is 800. The function y = 800 middot 3^x, where x is the number of 20 minute periods, the population growth. How many amoebas are in the petri dish after 3 hours? 16. A new car costs $15,000 to build in 2010. The company's financial analysts expect costs to rise by 6% per year for the 10 years they are planning to build the car. The cost to build the car can be modeled by the function f(t) = 15,000(1.06)^t, where t is the number of years after 2010. How much will it cost the company to build the car in 2017?

Explanation / Answer

Linear relation : y = mx +c

Exonential relation: y = a.b^x

1) (x, y) : (1 , 3) ( 2, 9) (3 , 27) (4 , 81)

slope between two consecutive points: (y2-y1)/(x2 -x2)

= 6/1 , 18/1 , 54/1   ( slope is not constant)

So, its not a linear function:

Exponential : Relation is exponential as y2/y1 = y3/y2 = 9/3 = 27/9 =81/27 = 3 constant

Hence exponential

2) (x , y) : (1, 3) (2, 9) (3,15) (4, 21)

slope between two consecutive points: (y2-y1)/(x2 -x2)

= 6/1 , 6/1 ,6/1 = slope constant

Its a linear relation

3) y = 5.2^x --- exponential

4) y = 6.x^3

Niether linear or exponential.Its a cubic polynomial

5) y = 3x -8

linear relation

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