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OverLord2011 [107]

3 years ago

10

Simplify (2^5/3^2)^4 A. 2^20/3^8 B. 2^9/3^8 C. 8^5/12^2 D. 2/3^2

1 answer:

ryzh [129]3 years ago

5 0

Hey there!

$\bold{Simplify: (\frac{2^5}{3^2})^4 }$

$\bold{2^5 = 32}$
$\bold{(\frac{32}{3^2})^4 }$
$\bold{3^2= 9}$
$\bold{(\frac{32}{9})^4 }$
$\bold{\frac{1,048,576}{6,561} }$
↑to sum it all up, your $\boxed{\boxed{\bold{Answer: A. \frac{2^2^0}{3^8} }}}$

Good luck on your assignment and enjoy your day!

~ $\bf{LoveYourselfFirst:)}$

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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

Delvig [45]

Answer:

B) 25

Step-by-step 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 :

$G=\frac{f(b)}{f(a)}$

We can check this by plugging in the given points.

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

$G=\frac{f(3)}{f(1)}$

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$f(1)=3(5)^1$

Plugging in values.

$G=\frac{3(5)^3}{3(5)^1}$

$G=\frac{(5)^3}{(5)^1}$ (On canceling the common terms)

$G=(5)^{(3-1)}$ (Using quotient property of exponents $\frac{a^b}{a^c}=a^{(b-c)}$ )

$G=(5)^{2}$

∴ $G=25$

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

$G=\frac{f(7)}{f(5)}$

$f(7)=3(5)^7$

$f(5)=3(5)^5$

Plugging in values.

$G=\frac{3(5)^7}{3(5)^5}$

$G=\frac{(5)^7}{(5)^5}$ (On canceling the common terms)

$G=(5)^{(7-5)}$ (Using quotient property of exponents $\frac{a^b}{a^c}=a^{(b-c)}$ )

$G=(5)^{2}$

∴ $G=25$

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

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