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The exponential function f(x) = 3(5)x grows by a factor of 25 between x = 1 and x = 3. What factor does it grow by between x = 5 and x = 7?

A) 5
B) 25
C) 125
D) 625

2 Answers

1 vote

Answer:

25 B

Explanation:

What the other person said.

User Bachsau
by
7.6k points
6 votes

Answer:

B) 25

Explanation:

Given exponential function:


f(x)=3(5)^x

The growth factor between
x=1 and
x=3 is 25.

To find the growth factor between
x=5 and
x=7

Solution:

The growth factor of an exponential function in the interval
x=a and
x=b is given by :


G=(f(b))/(f(a))

We can check this by plugging in the given points.

The growth factor between
x=1 and
x=3 would be calculated as:


G=(f(3))/(f(1))


f(3)=3(5)^3


f(1)=3(5)^1

Plugging in values.


G=(3(5)^3)/(3(5)^1)


G=((5)^3)/((5)^1) (On canceling the common terms)


G=(5)^((3-1)) (Using quotient property of exponents
(a^b)/(a^c)=a^((b-c)) )


G=(5)^(2)


G=25

Similarly the growth factor between
x=5 and
x=7 would be:


G=(f(7))/(f(5))


f(7)=3(5)^7


f(5)=3(5)^5

Plugging in values.


G=(3(5)^7)/(3(5)^5)


G=((5)^7)/((5)^5) (On canceling the common terms)


G=(5)^((7-5)) (Using quotient property of exponents
(a^b)/(a^c)=a^((b-c)) )


G=(5)^(2)


G=25

Thus, the growth factor remains the same which is =25.

User Sbrattla
by
8.0k points

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