Biologists use a formula to estimate the mass of a mammal's brain.

to test an individual's use of a certain mineral, a researcher injects a small amount of a radioactive form of that mineral in

LUCKY_DIMON [66]

Using derivatives, the rate of change of the mineral level with respect to time for 4 days is -0.012 mg/cm².

<h3>What is the missing information?</h3>

The function for the amount is missing, and is given by:

$C(t) = \frac{1}{2}(6t + 1)^{-\frac{1}{2}}$

The problems asks for the rate of change of the mineral level with respect to time for 4 days.

<h3>What is the rate of change after 4 days?</h3>

The rate of change after 4 days is given by:

C'(4).

Applying the chain rule, the derivative of C(t) is given as follows:

$C^{\prime}(t) = \frac{1}{2}(6t+1)^\prime \times -\frac{1}{2} \times (6t+1)^{-\frac{3}{2}}$

$C^{\prime}(t) = -\frac{3}{2}(6t+1)^{-\frac{3}{2}}$

When t = 4, we have that:

$C^{\prime}(4) = -\frac{3}{2}(6(4)+1)^{-\frac{3}{2}}$

$C^{\prime}(4) = -\frac{3}{2}(25)^{-\frac{3}{2}}$

Applying properties of exponents, we have that:

$(25)^{-\frac{3}{2}} = \left(\frac{1}{25}\right)^{\frac{3}{2}} = \frac{1}{\sqrt{25^3}} = \frac{1}{25\sqrt{25}} = \frac{1}{125}$

Hence:

$C^{\prime}(4) = -\frac{3}{2} \times \frac{1}{125}$

C'(4) = -0.012.

The rate of change of the mineral level with respect to time for 4 days is -0.012 mg/cm².

More can be learned about derivatives at brainly.com/question/23819325

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3 0

1 year ago

The Smith family went to the theater

Ivenika [448]

Answer:

3 adult tickets and 4 child tickets

Step-by-step explanation:

a + k = 7

a = 7 - k

12a + 9k = 72

12(7 - k) + 9k = 72

84 - 3k = 72

3k = 12

k = 4

a = 3

7 0

3 years ago

Which value of x makes the open sentence true? 10 +m2x< 15x-20? 0, 1, 2,3

Zielflug [23.3K]

x=3 if the m was a typo, idk what that means

3 0

3 years ago

(08.03)Consider the following pair of equations:

Alekssandra [29.7K]

I hope this makes some sence! The answer should be (3,2)

4 0

3 years ago

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Christina knits a scarf for each of her 7 friends. Altogether, the scarfs had a total length of 39.9 ft. if each scarf has the s

Vikki [24]

The length of each scarf knitted for the 7 friends given the total length of the scarf altogether is 5.7 ft

<h3>Length of each scarf</h3><h3 />

Number of friends = 7
Total length of scarf = 39.9 ft

Length of each scarf = Total length of scarf / Number of friends

= 39.9 ft / 7

= 5.7 ft

Therefore, the length of each scarf knitted for the 7 friends given the total length of the scarf altogether is 5.7 ft

Learn more about length:

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4 0

2 years ago