Which of the following exponential functions represent growth and which represent decay?a.   y=92⋅4x represents exponential  b. f(t)=61⋅(25)t represents exponential  c. w(r)=220⋅0.92r represents exponential  d.   g⁢(r)=2⋅106⋅1.18r represents exponential  e.   y=7⋅109⋅0.6z represents exponential  f. h(x)=130⋅(32)x represents exponential

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Asked Oct 1, 2019
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Which of the following exponential functions represent growth and which represent decay?

a.   y=92⋅4x represents exponential 

 

b. f(t)=61⋅(25)t represents exponential

 

 

c. w(r)=220⋅0.92r represents exponential 

 

d.   g⁢(r)=2⋅106⋅1.18r represents exponential 

 

e.   y=7⋅109⋅0.6z represents exponential 

 

f. h(x)=130⋅(32)x represents exponential 

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Expert Answer

Step 1

The exponential function f(x)=a(b)^x represents

a) growth if a>0 and b>1

b) decay if a>0 and 1<b<1

Step 2

We compare the given function by f(x)=a(b)^x and find a and b

In case A, B,D and F , a>0 and b>1, so the functions represent growth

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A)y 92(4)a=92,b 4 a 0, b >1 B)f() 61(25)a 61,b 25 a 0,b>1 D)g(r) 2.106(1.18)' a 2.106, b 1.18 a 0,b 1 F)h(x) 130(32)a130,b 32 a> 0,b>1

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Step 3

In case C and E , a>0 and 0<b<1, so the functions represent decay

...
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C)w (r) 220(0.92)a220, b 0.92 0,0 b<1 E)y 7.109(0.6)a= 7.109,b 0.6 a> a > 0,0b<1

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