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Gemiola [76]
3 years ago
7

How to find an exponential function with two points?

Mathematics
1 answer:
BabaBlast [244]3 years ago
6 0
Well u have a basic equation y=a • b^x
a is the initial amount
b is the growth factor
and x is the exponent

the first step is to make a chart with ur two points for example
(0,4) and (2,16)
so ur chart will be
x. | y.
0. | 4
2. | 16
next you find the difference between the x side so 0 to 2 is +2
then find the difference between the y side so 4 to 16 is +12
then put it into a fraction with y over x or y/x so 12/2 then simplified 6/1 or just 6.

6 is the growth factor
and to find a u have to go on the y column and find the first number so
a is 4
x is still x because it's 0 but if it was 2 then it would be x-2 so it can cancel
so the answer would be y=4 • 6^x
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Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. (assume that
Lilit [14]
Your sequence
  -8, 16/3, -32/9, 64/27
is a geometric sequence with first term -8 and common ratio
  (16/3)/(-8) = (-32/9)/(16/3) = -2/3

The general term an of a geometric sequence with first term a1 and ratio r is given by
  an = a1·r^(n-1)
For your sequence, this is
  an = -8·(-2/3)^(n-1)
6 0
3 years ago
Help with this question
Morgarella [4.7K]

Answer:

C) (x-3)(x+3)

Note:

Just a tip there is an app called Desmos where you can put in equations like this and it will graph them for you.

7 0
3 years ago
An area is approximated to be 14 in 2 using a left-endpoint rectangle approximation method. A right- endpoint approximation of t
USPshnik [31]
The trapezoidal approximation will be the average of the left- and right-endpoint approximations.

Let's consider a simple example of estimating the value of a general definite integral,

\displaystyle\int_a^bf(x)\,\mathrm dx

Split up the interval [a,b] into n equal subintervals,

[x_0,x_1]\cup[x_1,x_2]\cup\cdots\cup[x_{n-2},x_{n-1}]\cup[x_{n-1},x_n]

where a=x_0 and b=x_n. Each subinterval has measure (width) \dfrac{a-b}n.

Now denote the left- and right-endpoint approximations by L and R, respectively. The left-endpoint approximation consists of rectangles whose heights are determined by the left-endpoints of each subinterval. These are \{x_0,x_1,\cdots,x_{n-1}\}. Meanwhile, the right-endpoint approximation involves rectangles with heights determined by the right endpoints, \{x_1,x_2,\cdots,x_n\}.

So, you have

L=\dfrac{b-a}n\left(f(x_0)+f(x_1)+\cdots+f(x_{n-2})+f(x_{n-1})\right)
R=\dfrac{b-a}n\left(f(x_1)+f(x_2)+\cdots+f(x_{n-1})+f(x_n)\right)

Now let T denote the trapezoidal approximation. The area of each trapezoidal subdivision is given by the product of each subinterval's width and the average of the heights given by the endpoints of each subinterval. That is,

T=\dfrac{b-a}n\left(\dfrac{f(x_0)+f(x_1)}2+\dfrac{f(x_1)+f(x_2)}2+\cdots+\dfrac{f(x_{n-2})+f(x_{n-1})}2+\dfrac{f(x_{n-1})+f(x_n)}2\right)

Factoring out \dfrac12 and regrouping the terms, you have

T=\dfrac{b-a}{2n}\left((f(x_0)+f(x_1)+\cdots+f(x_{n-2})+f(x_{n-1}))+(f(x_1)+f(x_2)+\cdots+f(x_{n-1})+f(x_n))\right)

which is equivalent to

T=\dfrac12\left(L+R)

and is the average of L and R.

So the trapezoidal approximation for your problem should be \dfrac{14+21}2=\dfrac{35}2=17.5\text{ in}^2
4 0
3 years ago
Whats is 1+1+3+7+8+33542
Murljashka [212]

Answer:

33562, You could have used a calculator, or used your head, why

Step-by-step explanation:

7 0
3 years ago
Each of four test scores in Connie’s class is to be weighted equally. On the first three tests, Connie scored 80%, 90% and 95%.
Zanzabum

Answer:

95%is the answer

Step-by-step explanation:

7 0
3 years ago
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