1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
hammer [34]
4 years ago
8

The student population at Oak Mountain High School for a given year can be modeled by the function P(t)=550(1.12)^t , where t is

the number of years since 1995. How many students were there in 1995?
Mathematics
1 answer:
Anton [14]4 years ago
3 0

Answer:

There were 550 students in the school in the year 1995

Step-by-step explanation:

In this question, given the exponential equation, we are asked to calculate the number of students in a particular year.

The exponential equation expected to be used is given as;

P(t) = 550(1.12)^t

Now we are told that t is the number of years since 1995 and we are told to calculate the number of students in that same year 1995. Thus, the value of t would be 1995-1995 = 0

We substitute this value of t into the equation;

P(0) = 550(1.12)^0

Since anything raised to the power of zero is 1, then ;

P(0) = 550 * 1 = 550

You might be interested in
For the differential equation 3x^2y''+2xy'+x^2y=0 show that the point x = 0 is a regular singular point (either by using the lim
Svetlanka [38]
Given an ODE of the form

y''(x)+p(x)y'(x)+q(x)y(x)=f(x)

a regular singular point x=c is one such that p(x) or q(x) diverge as x\to c, but the limits of (x-c)p(x) and (x-c)^2q(x) as x\to c exist.

We have for x\neq0,

3x^2y''+2xy'+x^2y=0\implies y''+\dfrac2{3x}y'+\dfrac13y=0

and as x\to0, we have x\cdot\dfrac2{3x}\to\dfrac23 and x^2\cdot\dfrac13\to0, so indeed x=0 is a regular singular point.

We then look for a series solution about the regular singular point x=0 of the form

y=\displaystyle\sum_{n\ge0}a_nx^{n+k}

Substituting into the ODE gives

\displaystyle3x^2\sum_{n\ge0}a_n(n+k)(n+k-1)x^{n+k-2}+2x\sum_{n\ge0}a_n(n+k)x^{n+k-1}+x^2\sum_{n\ge0}a_nx^{n+k}=0

\displaystyle3\sum_{n\ge2}a_n(n+k)(n+k-1)x^{n+k}+3a_1k(k+1)x^{k+1}+3a_0k(k-1)x^k
\displaystyle+2\sum_{n\ge2}a_n(n+k)x^{n+k}+2a_1(k+1)x^{k+1}+2a_0kx^k
\displaystyle+\sum_{n\ge2}a_{n-2}x^{n+k}=0

From this we find the indicial equation to be

(3(k-1)+2)ka_0=0\implies k=0,\,k=\dfrac13

Taking k=\dfrac13, and in the x^{k+1} term above we find a_1=0. So we have

\begin{cases}a_0=1\\a_1=0\\\\a_n=-\dfrac{a_{n-2}}{n(3n+1)}&\text{for }n\ge2\end{cases}

Since a_1=0, all coefficients with an odd index will also vanish.

So the first three terms of the series expansion of this solution are

\displaystyle\sum_{n\ge0}a_nx^{n+1/3}=a_0x^{1/3}+a_2x^{7/3}+a_4x^{13/3}

with a_0=1, a_2=-\dfrac1{14}, and a_4=\dfrac1{728}.
6 0
4 years ago
The image of (-9,-4) after a reflection over the y-axis?
lidiya [134]

Answer:

The answer is (-4,9)

Step-by-step explanation:

When you reflect across y=-x the x and y coordinates switch places and change signs.

7 0
3 years ago
Find the length of x. help please !
andreyandreev [35.5K]

Answer:

x = 10

Step-by-step explanation:

Use CPCTC (Corresponding parts of congruent triangles are congruent).

Set the ratios:

\frac{6.5}{5} = \frac{6.5 + 6.5}{x}

First, simplify. Combine like terms:

\frac{6.5}{5} = \frac{13}{x}

Next, cross multiply.

5 * x * \frac{6.5}{5}  = \frac{13}{x} * x * 5\\x * 6.5 = 13 * 5\\6.5x = 65\\

Isolate the variable, x. Divide 6.5 from both sides of the equation:

\frac{(6.5x)}{6.5} = \frac{(65)}{6.5} \\\\x = \frac{65}{6.5}\\x =  10

Check:

\frac{5}{6.5} = \frac{x}{13}

Plug in 10 for x (Your answer). Cross multiply, then simplify:

\frac{5}{6.5} = \frac{10}{13}

13 * 6.5 * \frac{5}{6.5} = \frac{10}{13} * 13 * 6.5

13 * 5 = 10 * 6.5

65 = 65 (True).

~

6 0
3 years ago
Solve and graph 4<-1/3n
Liula [17]

Answer:

n<-12

Step-by-step explanation:

4<-1/3n

4<-n/3

4×3<-n

12<-n

-12<n

n<-12

5 0
3 years ago
If represented in a stem and leaf plot, what would be the leaf of the number 329?​
sdas [7]

Answer:

You can either do a back to back stem and leaf plot, where you would have double the values. In a normal stem and leaf plot you would just have one set of 3's where you would put all the values that start with 3 in that column. A back to back is the same but instead you would have two 3 values, where anything that is higher than 5 would be in the second value of 3, but anything lower would be in that first value of 3.

4 0
4 years ago
Other questions:
  • The value of "x" in the attached figure is: *
    10·1 answer
  • Solve the equation below for the exact values of 4x2-5=75 ​
    8·1 answer
  • Liam makes fruit punch bye mixing orange and pineapple juice. How much fruit punch does he make in all?
    15·1 answer
  • Whatt does the square root symbol with 47 lie with a scale from 1 to 10
    6·1 answer
  • Please help me on this <br><br> Simplify (12^2)^4
    12·1 answer
  • rachel wants to put her dog tutu, outside in the backyard. she ties a 13 ft rope around the magnolia tree in the yard. the rope
    6·1 answer
  • 3х + 4 = 9x - 8<br> What is the value of X to make the equation true?
    12·1 answer
  • Write a word phrase for the algebraic expression. 6+(x x 3)
    5·1 answer
  • Alyssa makes $14 baby sitting on Monday, $15.50 baby sitting on Tuesday, spends $24.35 at the
    10·1 answer
  • If you start off with 1220 and you take away 100 then add 50 how much do you have
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!