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## PowerPoint Slideshow about ' Exponential Function 5 Item MCQ' - aubrey-cash

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1. Which of the following define an exponential function?

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a) 2x2 + 3x – 6= 8

b) 2/3 m – 5 = 15

c) y = 2x + 1

d) p3 + 2p -3 = 0

Exponential Function

Definition:

→ If a>0 and a ≠ 1,then the exponential function with the base a is a function defined by f(x) = ax, where x is any real numbers.

→ therefore y= 2x +1 is the only equation wherein the exponent x vary.

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Graph of Exponential Function

The graph of y = ax is upward-sloping, and

increases faster as x increases. The graph

always lies above the x-axis but can get

arbitrarily close to it for negative x; thus,

the x-axis is a horizontal asymptote. The

slope of the graph at each point is equal

to its y coordinate at that point.

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- Solution

93x = (1/3)5-x

32(3x)= 3-1(5-x) change the equation with same base

6x = -5+x bring down the exponents

5x = -5 solve for x

x = -1 answer

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4) A certain city has a population of 20000 and a growth rate of 3.5%.What will be the expected population after 3 years?

- 24,145
- 23,501
- 23,219
- 22,174

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The Exponential Growth is in the form

Y = P( 1 + r)xwhere P = original number

r = rate of change

x = unit of time

y = total number after x years

So, P = 20000 r = 3.5% or 0.035 t = 3 years

Substitute Y = P( 1 + r)x

= 20,000 (1 + .035)3

= 20,000 (1.035)3

= 20,000 (1.1087)

= 22,174 expected population after 3 yrs

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5) If a car depreciates at an annual rate of 15%, how much would be its value at the end of two years if its cost is $450,000 when new? a) $325,125 b) $276,356c) $315,134d) $412,300

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The Exponential Decay is in the form

Y = P( 1 - r)xwhere P = original amount

r = rate of change

x = unit of time

y = total amount after x years

So, P= $450,000 r = 15% or 0.15 t= 2 years

Substitute Y = P( 1 - r)x

= 450,000 (1 - .15)2

= 450,000 (0.85)2

= 450,000 (0.7225)

= $325,125 amount of car after 2 years

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