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mina [271]
3 years ago
7

Following the lead of the National Wildlife Federation, the Department of the Interior of a South American country began to reco

rd an index of environmental quality that measured progress and decline in the environmental quality of its forests. The index for the years 2004 through 2014 is approximated by the functionI I(t) = 1/3t^3 − 5/2t^2 + 80 (0 ≤ t ≤ 10) where t = 0 corresponds to 2004. For what years is the quality of the forests in this country improving?
Mathematics
1 answer:
chubhunter [2.5K]3 years ago
7 0

Answer:

After 2009 the quality of the forests in this country improving.

Step-by-step explanation:

Consider the provided function.

f(t) = \frac{1}{3}t^3-\frac{5}{2}t^2 + 80

f'(t) = t^2-5t

Substitute f'(t)=0.

t^2-5t=0

t(t-5)=0

t=0\ or\ t=5

It is given that  (0 ≤ t ≤ 10)

The test interval are (0,5) and (5,10)

For (0 < t < 5) the value of f'(t)

For (5 < t < 10) the value of f'(t) >0

Hence, the function is increasing from (5,10).

t = 0 corresponds to 2004.

Therefore, after 2009 the quality of the forests in this country improving.

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A college student has 700$ in their account she spends $165 from the account on books and then deposits $190 in the account how
adell [148]

Hello,

I hope so far you and your family are staying safe and healthy!

We need to solve this step by step.

The college student has $700 in their account.  But then she spends $165 on books from that money. So we need to Subtract that.

700 - 165 =535

However, later on, she deposits $190 to the same account. So we need to take the remain we had and add it to the new amount.

535 + 190 = 725

Thus,

There are $725 in the account.

I wish you all the best!

~Gary

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Need help for4,5,6 dealing with isosceles triangles
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Step-by-step explanation:

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