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which function below represents exponential decay?ƒ(x) = 0.5(2)xƒ(x) = 4(0.25)xƒ(x) = 2(1.3)xƒ(x) = (-3)x

User Tom Prats
by
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2 Answers

6 votes

Answer:

Option 2 -The function represent the exponential decay is
f(x) = 4(0.25)^x

Explanation:

To find : Which function below represents the exponential decay.

Solution :

The exponential function is in the form
y=a(b)^t

where a is the initial value a≠0 and b is the growth or decay factor b>0, b≠0

If the function is exponentially grow then b>1

If the function is exponentially decay then b<1

Now we check given functions by comparing the given exponential function and note the nature of b.

1)
f(x) = 0.5(2)^x

a=0.5 , b=2>1

Exponentially grow

2)
f(x) = 4(0.25)^x

a=4 , b=0.25<1

Exponentially decay

3)
f(x) = 2(1.3)^x

a=0.5 , b=1.3>1

Exponentially grow

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

a=1 , b=-3 (negative)

Does not exist

Therefore, Option 2 - The function represent the exponential decay is
f(x) = 4(0.25)^x

User HongyanShen
by
6.6k points
1 vote
the one with the fraction in the parenthasees

remember
F=P(r)^t
in decay, r<1
in growth, r>1
and r is positive so we don't have wierd fliping values

answer would be f(x)=4(0.25)^x

2nd one is answer

User Rahul L
by
6.6k points