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2 years ago

Solve the following exponential equation:5^x=2 e^x=10

Mathematics

1 answer:

olya-2409 [2.1K]2 years ago

3 0

Number 1.

$5^x=2$ , first we will take the $log$ of both of these numbers getting us,

$x=\frac{log(2)}{log(5)}$ , which then gives us that $x=0.4306777777....$

Number 2

$e^x=10$ , solve for our exponent, $2.718282^x=10$ , use the logarithmic formula, and we get,

$x=\frac{log(10)}{log(2.718282)}$ , which then we get that $x=2.302585$

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Find two numbers whose product is -2, and whose sum is -1.

PIT_PIT [208]

Answer:

$x=-2 \ \ \ and \ \ \ y=1$

Step-by-step explanation:

Suppose numbers are x and y

Product of x and y is -2

$xy=-2$

And sum of x and y is -1

$x+y=-1$

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2 years ago

an angle bisector of a triangle divides the opposite side of the triangles into segments 6cm and 4cm long. A second side of tria

Dovator [93]

From the angle bisector theorem
we can first assume the third side is x, therefore
7.4/6 = x/4
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x = 4.93 cm
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3 years ago

1. The number of rabbits on an island is increasing exponentially.

Zina [86]

Answer:

There are approximately 114 rabbits in the year 10

Step-by-step explanation:

Exponential Growth

The natural growth of some magnitudes can be modeled by the equation:

$P=P_o(1+r)^t$

Where P is the actual amount of the magnitude, Po is its initial amount, r is the growth rate and t is the time.

We are given two measurements of the population of rabbits on an island.

In year 1, there are 50 rabbits. This is the point (1,50)

In year 5, there are 72 rabbits. This is the point (5,72)

Substituting in the general model, we have:

$50=P_o(1+r)^1$

$50=P_o(1+r)\qquad\qquad[1]$

$72=P_o(1+r)^5\qquad\qquad[2]$

Dividing [2] by [1]:

$\displaystyle \frac{72}{50}=(1+r)^{5-1}=(1+r)^{4}$

Solving for r:

$\displaystyle r=\sqrt[4]{\frac{72}{50}}-1$

Calculating:

r=0.095445

From [1], solve for Po:

$\displaystyle P_o=\frac{72}{(1+r)^5}$

$\displaystyle P_o=\frac{72}{(1.095445)^5}$

$P_o=45.64355$

The model can be written now as:

$P=45.64355(1.095445)^t$

In year t=10, the population of rabbits is:

$P=45.64355(1.095445)^{10}$

P = 113.6

$P\approx 114$

There are approximately 114 rabbits in the year 10

5 0

2 years ago

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Answer:
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8 0

2 years ago

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3 years ago

Solve the following exponential equation:5^x=2 e^x=10​

Solve the following exponential equation:5^x=2 e^x=10