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nlexa [21]
3 years ago
11

Write an exponential function to model the situation. A population of 470 animals decreases at an annual rate of 12%.

Mathematics
1 answer:
Tamiku [17]3 years ago
5 0
\bf \qquad \textit{Amount for Exponential Decay}
\\\\
A=P(1 - r)^t\qquad 
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{initial amount}\to &470\\
r=rate\to 12\%\to \frac{12}{100}\to &0.12\\
t=\textit{elapsed time}\\
\end{cases}
\\\\\\
A=470(1-0.12)^t\implies A=470(0.88)^t
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ICE Princess25 [194]

Answer:

11

Step-by-step explanation:

The median is the number in the middle :)

8 0
4 years ago
Determine the inverse of the function f(x) = log3(4x + 5) − 6.
beks73 [17]

Answer:

f inverse of x is equal to 3 to the power of the quantity x plus 6 end quantity minus 5 all over 4

Step-by-step explanation:

The function f(x)=\log_3 (4x+5)-6 can be thought of as a series of steps, one operation at a time:

Start with x

Multiply by 4

Add 5

Take the \log_3

Subtract 6

That gives you a function value f(x).

To get the inverse function, read that list from the bottom up (in reverse order, using inverse operations at each step).

Start with x  (a bit confusing, because this  x  represents the function value you get at the end of the above list).

Add 6   (add is the inverse operation of subtract)

Raise 3 to the ...    3^{\text{result of previous step}

Subtract 5

Divide by 4

f^{-1}(x) = \frac{3^{x+6}-5}{4}

Let's test this out.  Find f(1).

f(1)=\log_3(4 \cdot 1 + 5)-6 =\log_3(9)-6=2-6=-4

Now put -4 into the inverse function.

f^{-1}(-4)=\frac{3^{-4+6}-5}{4}=\frac{3^2-5}{4}=\frac{9-5}{4}=\frac{4}{4} =1

The final result is the number we started with when we put 1 into <em>f</em>(<em>x</em>).

Finding an inverse is reversing the action of the function  <em>f</em>  by doing inverse operations in "backwards" order.

A lot of authors have you do this by switching  x  and  y  in the formula for a function, then solving for  <em>x</em>.

y = \log_3(4x+5)-6\text{  switch x and y}\\\\x = \log_3(4y+5)-6\\\\x+6 = \log_3(4y+5)\\\\3^{x+6}=4y+5\\\\3^{x+6}-5=4y\\\\\frac{3^{x+6}-5}{4}=y

4 0
2 years ago
In triangle △JKL, ∠JKL is right angle, and KM is an altitude. JK=24 and JM=18, find JL.
PolarNik [594]

Answer:

JL ≈ 32  

Step-by-step explanation:

The triangle JKL  has a side of JK = 24 and we are asked to find side JL. The triangle JKL is a right angle triangle.

Let us find side the angle J first from the  triangle JKM. Angle JMN is 90°(angle on a straight line).

using the cosine ratio

cos J = adjacent/hypotenuse

cos J = 18/24

cos J = 0.75

J = cos⁻¹ 0.75

J = 41.4096221093

J ≈ 41.41°

Let us find the third angle L of the triangle JKL .Sum of angle in a triangle = 180°. Therefore,  180 - 41.41 - 90 = 48.59

Angle L = 48.59 °.

Using sine ratio

sin 48.59 ° = opposite/hypotenuse

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cross multiply

JL sin 48.59 ° = 24

divide both sides by sin 48.59 °

JL = 24/sin 48.59 °

JL = 24/0.74999563751

JL = 32.0001861339

JL ≈ 32  

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Answer:32

Step-by-step explanation:

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