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Oliga [24]
3 years ago
11

A quantity with an initial value of 870 decays exponentially at a rate of 0.55% every 4 decades. What is the value of the quanti

ty after 85 decades, to the nearest hundredth?

Mathematics
1 answer:
Veseljchak [2.6K]3 years ago
8 0

Step-by-step explanation:

Below is an attachment containing the solution.

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Determine whether each expression is equivalent to 49^2t – 0.5.
vampirchik [111]

Answer:

None of the expression are equivalent to 49^{(2t - 0.5)}

Step-by-step explanation:

Given

49^{(2t - 0.5)}

Required

Find its equivalents

We start by expanding the given expression

49^{(2t - 0.5)}

Expand 49

(7^2)^{(2t - 0.5)}

7^2^{(2t - 0.5)}

Using laws of indices: (a^m)^n = a^{mn}

7^{(2*2t - 2*0.5)}

7^{(4t - 1)}

This implies that; each of the following options A,B and C must be equivalent to 49^{(2t - 0.5)} or alternatively, 7^{(4t - 1)}

A. \frac{7^{2t}}{49^{0.5}}

Using law of indices which states;

a^{mn} = (a^m)^n

Applying this law to the numerator; we have

\frac{(7^{2})^{t}}{49^{0.5}}

Expand expression in bracket

\frac{(7 * 7)^{t}}{49^{0.5}}

\frac{49^{t}}{49^{0.5}}

Also; Using law of indices which states;

\frac{a^{m}}{a^n} = a^{m-n}

\frac{49^{t}}{49^{0.5}} becomes

49^{t-0.5}}

This is not equivalent to 49^{(2t - 0.5)}

B. \frac{49^{2t}}{7^{0.5}}

Expand numerator

\frac{(7*7)^{2t}}{7^{0.5}}

\frac{(7^2)^{2t}}{7^{0.5}}

Using law of indices which states;

(a^m)^n = a^{mn}

Applying this law to the numerator; we have

\frac{7^{2*2t}}{7^{0.5}}

\frac{7^{4t}}{7^{0.5}}

Also; Using law of indices which states;

\frac{a^{m}}{a^n} = a^{m-n}

\frac{7^{4t}}{7^{0.5}} = 7^{4t - 0.5}

This is also not equivalent to 49^{(2t - 0.5)}

C. 7^{2t}\ *\ 49^{0.5}

7^{2t}\ *\ (7^2)^{0.5}

7^{2t}\ *\ 7^{2*0.5}

7^{2t}\ *\ 7^{1}

Using law of indices which states;

a^m*a^n = a^{m+n}

7^{2t+ 1}

This is also not equivalent to 49^{(2t - 0.5)}

6 0
3 years ago
Write an expression so that when u divided 1/4 by a number the answer will be larger
Viktor [21]
20x1/4=5
Think thats what you mean
4 0
3 years ago
Sonny plotted the point (1,6) and used the slope -2 to find another point on the line. Which point could be the one that Sonny f
Dmitrij [34]

Answer:

2,4

Step-by-step explanation:

I could be wrong but the equation would be 6-2 and 1+1

7 0
2 years ago
Read 2 more answers
6 1/4 as a decimal number
Musya8 [376]
Answer- 6.25 Your welcome.
4 0
3 years ago
Read 2 more answers
Factor the mn+5m-3n-15
neonofarm [45]
The factor of mn+5m-3n-15 is 6m-4n-15.
3 0
3 years ago
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