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# Does each equation represent exponential decay or exponential growth?

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Does each equation represent exponential decay or exponential growth?

Drag and drop the choices into the boxes to correctly complete the table.

Note: If an equation is neither exponential growth nor exponential decay, do not drag it to the table.

Here are the options

g(x)=0.3(x)

H=72(56)^t

A=(43)^t

H=5.9(0.82)^t

y=0.8(3.6)^t

f(t)=0.72(15)^t

A=49(8)^t

Nov 7, 2018

#1
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Remember that in the form

a(b)^x       where  a > 0

When   b > 0  but < 1.....we have a decay function

When   b > 1.....we have a growth function

BTW..."a"  doesn't matter in the determination of these.....only the value of  b

So

g(x)=0.3(x)      this  is neither ...we have no exponent [ it's linear ]

H=72(56)^t     growth  b  = 56

A=(43)^t        growth   b  = 43    [ "a" is an understood "1"  ]

H=5.9(0.82)^t      decay       b =  0.82

y=0.8(3.6)^t      growth   b = 3.6

f(t)=0.72(15)^t    growth    b  = 14

A=49(8)^t      growth  b  = 8

Does this make sense, Jenny   ???   Nov 7, 2018
edited by CPhill  Nov 7, 2018
#2
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Some of these were fraction, i put the choices in wrong would the answers change ?

here is the correct choices

g(x)=0.3(x)

H=7/2(5/6)^t

A=(4/3)^t

H=5.9(0.82)^t

y=0.8(3.6)^t

f(t)=0.72(15)^t

A=4/9(8)^t

jjennylove  Nov 7, 2018
#3
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H=(7/2)(5/6)^t       decay     (  b  = 5/6   )

And as long as the last one  is   (4/9) (8)^t   it is still growth   Nov 7, 2018
edited by CPhill  Nov 7, 2018
#4
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Note that   A = (4/3)^t  is still growth, too....b > 1   CPhill  Nov 7, 2018
#5
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It only matters about whether or not the number instead the parentheses is greater or less than 1 ? to determine the answer?

Nov 7, 2018
#6
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Yep...[.as long  as we have an exponent  on "b"  and "a" is positive ]

So......

a (b)^x       is decay  if     0 < b < 1

And  growth   if  b > 1   CPhill  Nov 7, 2018
edited by CPhill  Nov 7, 2018
#7
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Got it! Thank you jjennylove  Nov 7, 2018
edited by jjennylove  Nov 7, 2018
#8
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I was wondering if theres anyway you could help me with some algebra questions ?

jjennylove  Nov 9, 2018