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3 years ago

9.2.8.

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We have been given that the number of students enrolled at a college is 18,000 and grows 4% each year. We are asked to find number of students after 22 years.

We will use exponential growth function to solve our given problem.

We know that an exponential growth function is in form $y=a\cdot (1+r)^x$ , where

y = Final value,

a = Initial value,

r = Growth rate in decimal form,

x = Time

$4\%=\frac{4}{100}=0.04$

$y=18,000\cdot (1+0.04)^x$

$y=18,000\cdot (1.04)^x$

To find number of students after 22 years, we will substitute $x=22$ in our function.

$y=18,000\cdot (1.04)^{22}$

$y=18,000\cdot (2.3699187915049464)$

$y=42,658.53824$

$y\approx 42,659$

Therefore, there will be approximately 42,659 students after 22 years.

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The radius of a right circular cone is increasing at a rate of 1.9 in/s while its height is decreasing at a rate of 2.2 in/s. At

musickatia [10]

Answer:

Volume of the cone is increasing at the rate $9916\pi \frac{in^3}{s}$ .

Step-by-step explanation:

Given: The radius of a right circular cone is increasing at a rate of $1.9$ in/s while its height is decreasing at a rate of $2.2$ in/s.

To find: The rate at which volume of the cone changing when the radius is $134$ in. and the height is $136$ in.

Solution:

We have,

$\frac{dr}{dt} =1.9 \:\text{in/s}$ , $\frac{dh}{dt}=-2.2\:\text{in/s}$ , $r=134 \:\text{in}$ , $h=136\:\text{in}$

Now, let $V$ be the volume of the cone.

So, $V=\frac{1}{3}\pi r^{2}h$

Differentiate with respect to $t$ .

$\frac{dv}{dt} =\frac{1}{3}\pi \left [ r^2\frac{dh}{dt}+h\left ( 2r \right )\frac{dr}{dt} \right ]$

Now, on substituting the values, we get

$\frac{dv}{dt} =\frac{1}{3}\pi\left [ \left ( 134 \right )^2\left ( -2.2 \right )+\left ( 136\right )\left ( 2 \right )\left ( 134 \right )\left ( 1.9 \right ) \right ]$