You are right in thinking that the base of the logarithm doesn't matter. It only affects the spread of the data points if you were to plot them, but would not ultimately have any effect on the slope of the line (but it would on the y-intercept).
One major discrepancy I'm noticing is in the values you found for 
. For example, if 
, then you should have 
. Not sure how you got -7.0, and the same goes for the rest of your table of values.
Another thing is that the provided solution suggests you take the average the first and last pairs of consecutive data points, and use these values in the slope formula to obtain the best-fit line's slope. If that's the case, then you should have
(i.e. you have to take the average of the given values, then use those averages in the 
expressions - but this doesn't significantly affect the slope you found)
Ultimately, I think the problem is that your expression for the slope appears to be 
, when the solution says it should be the reciprocal. I'm of the opinion that your slope is correct, since the experiment refers to 
(and hence 
) as the independent variable, and so 
would serve as the "run" and 
would serve as the "rise".
Let <em>a</em> be the first term in the sequence. If <em>r</em> is the ratio between consecutive terms, then the second term is <em>ar</em>, the third term is <em>ar </em>^2, the fourth is <em>ar</em> ^3, and so on, up to the <em>n</em>-th term <em>ar</em> ^(<em>n</em> - 1).
So the third, fourth, and fifth terms are such that
<em>ar</em> ^2 = 18
<em>ar</em> ^3 = 27
<em>ar</em> ^4 = 81/2
Solve for <em>a</em> and <em>r</em> :
(<em>ar</em> ^3) / (<em>ar</em> ^2) = 27/18 => <em>r</em> = 3/2
<em>ar</em> ^2 = <em>a</em> (3/2)^2 = 9/4 <em>a</em> = 18 => <em>a</em> = 8
Then the <em>n</em>-th term in the sequence is
<em>ar</em> ^(<em>n</em> - 1) = 9 (3/2)^(<em>n</em> - 1)
You can rewrite this by first rewriting 9 = 3^2, then
9 (3/2)^(<em>n</em> - 1) = 3^2 * 3^(<em>n</em> - 1) / 2^(<em>n</em> - 1) = 3^(<em>n</em> + 1)/2^(<em>n</em> - 1)
Answer:
Yes (3,9) is a solution.
Step-by-step explanation:
Substitute 9 for y and 3 for x then do the equation and you should get 9=9 for both.
Answer:
La respuesta esta abajo
Step-by-step explanation:
La pregunta no está completa porque no contiene gráficos, pero te mostraré cómo responderla.
La ecuación de un gráfico de línea recta viene dada por:
y = mx + b; donde y y x son variables, m es la pendiente de la gráfica y b es la intersección en y (que es el valor de y cuando x es 0)
Dado que la ecuación de la gráfica es y = mx, comparando con la ecuación de una línea recta (y = mx + b), podemos concluir que la gráfica con una ecuación y = mx, tiene una pendiente de my una intersección con y de 0.
Esto significa que la gráfica pasa por el origen sin tocar el eje y. Además, la gráfica tiene una pendiente positiva.
.27 repeating is 3/11
The standard notation for a repeating decimal is to put a bar over the repeating digits, that is, <span>0.27272727...=0.27 repeating
</span>
