All categories

2 years ago

B(1)= 160, b(n) = b(n-1) * 0.5 for n (g/e) 2 determine the first 4 items in a sequence given this recursive formula.

Mathematics

1 answer:

Paul [167]2 years ago

7 0

Answer:

160

Step-by-step explanation:

You start with the first term that is given which would be

b(1)=160

That would be our first term, then we multiply by 0.5 which would be 1/2

which gives us 80 as it is a division

You take the next term that we have found (80) and then we do the same thing, multiply by 0.5 (1/2)

You might be interested in

Enter the solutions from least to greatest. (2x+4)(3x-2)=0

MArishka [77]

Answer:

From least to greatest: -2, 2/3

Step-by-step explanation:

Set each factor equal to 0 and solve

2x + 4 =0

2x = -4

x = -2

3x - 2 = 0

3x = 2

x = 2/3

4 0

2 years ago

If (x+2) is a factor of x^3-6x^2+kx+10, k=

Alja [10]

If a binomial $(x-a)$ is a factor of a polynomial, then $a$ is a root of this polynomial.

$(x+2)=(x-(-2)) \Rightarrow a=-2\\\\
(-2)^3-6\cdot(-2)^2+k\cdot(-2)+10=0\\
-8-24-2k+10=0\\
-2k=22\\\
\boxed{k=-11}
$

3 0

3 years ago

How much would $100 invested at 8% intrest compounded annually be worth after 15 years? round your answer to the nearest cent. d

frosja888 [35]

Our P = 100, r = .08, n = 1 (annually means once a year), and t = 15. Filling in accordingly, we have $A(t)=100(1+ \frac{.08}{1})^{(1)(15)}$ . Simplifying a bit gives us $A(t)=100(1+.08)^{15}$ and $A(t)=100(1.08)^{15}$ . Raising that number inside the parenthesis to the 15th power gives us $A(t)=100(3.172169114)$ . Multiplying to finish means that A(t) = $317.22

3 0

4 years ago

A population of bees is decreasing. The population in a particular region this year is 1,250. After 1 year, it is estimated tha

8_murik_8 [283]

To model this situation, we are going to use the decay formula: $A=Pe^{rt}$
where
$A$ is the final pupolation
$P$ is the initial population
$e$ is the Euler's constant
$r$ is the decay rate
$t$ is the time in years

A. We know for our problem that the initial population is 1,250, so $P=1250$ ; we also know that after a year the population is 1000, so $A=1000$ and $t=1$ . Lets replace those values in our formula to find $r$ :
$A=Pe^{rt}$
$1000=1250e^{r}$
$e^{r}= \frac{1000}{1250}$
$e^{r}= \frac{4}{5}$
$ln(e^{r})=ln( \frac{4}{5} )$
$r=ln( \frac{4}{5} )$
$r=-02231$

Now that we have $r$ , we can write a function to model this scenario:
$A(t)=1250e^{-0.2231t}$ .

B. Here we are going to use a graphing utility to graph the function we derived in the previous point. Please check the attached image.

C.
- The function is decreasing
- The function doe snot have a x-intercept
- The function has a y-intercept at (0,1250)
- Since the function is decaying, it will have a maximum at t=0:
$A(0)=1250e^{(-0.2231)(0)$
$A_{0}=1250e^{0}$
$A_{0}=1250$
- Over the interval [0,10], the function will have a minimum at t=10:
$A(10)=1250e^{(-0.2231)(10)$
$A_{10}=134.28$

D. To find the rate of change of the function over the interval [0,10], we are going to use the formula: $m= \frac{A(0)-A(10)}{10-0}$
where
$m$ is the rate of change
$A(10)$ is the function evaluated at 10
$A(0)$ is the function evaluated at 0
We know from previous calculations that $A(10)=134.28$ and $A(0)=1250$ , so lets replace those values in our formula to find $m$ :
$m= \frac{134.28-1250}{10-0}$
$m= \frac{-1115.72}{10}$
$m=-111.572$
We can conclude that the rate of change of the function over the interval [0,10] is -111.572.

7 0

3 years ago

Terry needs to carry a pole that

Natasha2012 [34]

Answer:

Yes, The pole will fit through the door because the diagonal width of the door is 10.8 feet, which is longer than the length of the pole.

Step-by-step explanation:

Using the Pythagorean Theorem, ( $a^2+b^2=c^2$ ) we can measure the hypotenuse of a right triangle. Since the doorway is a rectangle, and a rectangle cut diagonally is a right triangle, we can use Pythagorean Theorem to measure the diagonal width of the doorway.

Plug in the values of the length and width of the door for a and b. The c value will represent the diagonal width of the doorway:

$6^2+9^2=c^2$

$36+81=c^2$

$117=c^2$

Since 117 is equal to the value of c multiplied by c, we must find the square root of 117 to find the value of c.

$\sqrt{117} =10.8$

$10.8=c$

Yes, The pole will fit through the door because the diagonal width of the door is 10.8 feet, which is longer than the length of the pole, measuring 10 feet.

7 0

3 years ago