Question

How does f(x) = 10x change over the interval from x = 5 to x = 6?

A) f(x) increases by 100%
B) f(x) increases by 500%
C) f(x) increases by 900%
D) f(x) increases by 1000%

Answer 1

f(x) increases by 900%

Explanation:

f(x) increases by 900%

f(5) = 105

f(6) = 106

f(6)

f(5)

=

106

105

= 106−5 = 10

Therefore, f(x) increases by a factor of 10 over the interval from x = 5 to x = 6.

Then,

A value increases by p% if it changes by a factor of 1 +

p

100

.

f(6) = 10f(5)

f(6) = (1 + 9)f(5)

f(6) = (1 +

900

100

)f(5)

f(6) = f(5) +

900

100

f(5)

f(6) = f(5) + 900% · f(5)

Thus, f(6) is 900% larger than f(5). So, f(x) increases by 900% over the interval from x = 5 to x = 6.

Answer 2

C.
`900 \%`

Explanation:

The given function is

`f(x)=10^x`

Substitute x=5 to get;

`f(5)=10^5=100000`

Substitute x=6 to get;

`f(5)=10^6=1000000`

The percentage increment of
`f(x)` over the interval from x=5 to x=6 is

`=(100000-100000)/(10000)*100 \%`

`=(900000)/(10000)*100 \%`

`=9*100 \%`

`=900 \%`