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

Answer:

C. $900 \%$

Step-by-step 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

$=\frac{100000-100000}{10000}\times100 \%$

$=\frac{900000}{10000}\times100 \%$

$=9\times100 \%$

$=900 \%$

Answer 2

Answer:

f(x) increases by 900%

Step-by-step 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.