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Marat540 [252]
3 years ago
13

A scientist has a sample of the radioactive isotope bismuth-212. The isotope decays exponentially as shown in the table. Time (s

econds) Mass (grams) 10 26.8 20 23.9 30 21.3 40 19.0 50 16.9 60 15.1 Which equation best represents the curve of best fit for this set of data? A. f(x) = 29 • 0.989x B. f(x) = 27 • 1.011x C. f(x) = 30 • 0.989x D. f(x) = 28 • 0.234x
Mathematics
1 answer:
luda_lava [24]3 years ago
7 0

Answer:

f(x) = 30 • 0.989x

Step-by-step explanation:

Given the data :

10 26.8

20 23.9

30 21.3

40 19

50 16.9

60 15.1

Using technology, the exponential model equation obtained by plotting the data is :

y = 30.068(0.989)^x

Based on the general exponential formula :

y = ab^x

y = predicted value

Initial value, a = 30.068

Rate = b = 0.989

The most appropriate model equation from the options given is :

f(x) = 30 • 0.989^x

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Determine (without solving the problem) an interval in which the solution of the given initial value problem is certain to exist
charle [14.2K]

Answer: t = - 5 ∈ I_{1} = ( -∞ , -4 )

Step-by-step explanation:

The standard form of O.D.E is written as :

y^{1} + p(t) = g(t)

Equation given :

(16-t^{2} )y^{1} + 9ty = 5t^{2} ,       y(-5) = 1

The first thing to do is to write the O.D.E in standard form , that is we will divide through by 16 - t^{2} , so we have

y^{1} + \frac{9ty}{16-t^{2}}=\frac{5t^{2}}{16-t^{2}}

With this , we can see that p(t) and g(t) are both continuous in the same domain. Therefore , the intervals are :

I_{1} = ( -∞ , -4 )

I_{2} = ( - 4 , 4 )

I_{3} = ( 4 , -∞ )

recall that y(−5) = 1 , then t = -5

This means that :

t = - 5 ∈ I_{1} = ( -∞ , -4 )

3 0
3 years ago
1
VARVARA [1.3K]
<h3>Solution</h3>

\begin{aligned}\frac{1}{h-5}+\frac{2}{h+5}&=\frac{16}{h^2-25}\\\frac{(h+5)+2(h-5)}{(h-5)(h+5)}&=\frac{16}{h^2-25}\\\frac{h+2h+5-10}{h^2-25}&=\frac{16}{h^2-25}\\\frac{3h-5}{\cancel{h^2-25}}&=\frac{16}{\cancel{h^2-25}}\\3h-5&=16\\3h&=16+5\\3h&=21\\h&=\frac{21}{3}\\h&=7\end{aligned}

3 0
3 years ago
Can someone please help I need a clear explanation on how to solve this equation.
nikitadnepr [17]
B = amount of students who chose Bulldog

n = amount of students who chose lion

t = amount of students who chose tiger

so.. "t" chose tiger, ok

"<span>Four times as many students chose Bulldog as chose Tiger"
namely, if "t" chose tiger, then 4 times that many chose Bulldog, thus

b = 4t

"</span><span>Twice as many students chose Lion as chose Tiger"
namely, if "t" students chose tiger, twice as many chose lion

n = 2t

now, we know a total of 273 students were surveyed, thus

</span>\bf \begin{cases}&#10;b+n+t=273\\&#10;\boxed{4t}+\boxed{2t}+t=273&#10;\end{cases}&#10;\\\\\\&#10;7t=273\implies t=\cfrac{273}{7}\impliedby \textit{that many chose \underline{tiger}}<span>
</span>
6 0
4 years ago
Read 2 more answers
There are 35 squares shaded in a 50 square grid. What percentage of the grid is shaded?
Mumz [18]

Answer:

70%

Step-by-step explanation:

We can first find the fraction

35/50

We know that percent is out of 100 so multiply the top and bottom by 100

35/50 * 2/2 = 70/100

The percent is 70%

6 0
2 years ago
Read 2 more answers
Write an expression that represents the perimeter of the triangle.
uysha [10]

Answer:

(3m - 2) + (2m + 7) + (5m - 3)

Step-by-step explanation:

Perimeter is found by combining all side measurements together to find the total measurement. In this case, combine the sides:

(3m - 2) + (2m + 7) + (5m - 3) is your answer.

If you need a simplified expression, simply combine all the like terms together. Like terms are terms with the same as well as same amount of variables:

(3m + 2m + 5m) + (7 - 2 - 3)

(10m) + (2)

10m + 2 is your answer.

~

7 0
3 years ago
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