Please help asap 15 pts
2 answers:
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The graph of the given function is attached showing characteristics of the function.
The correct responses are;
- (a) F'(4) = -30 means that <u>on day 4, the number of fish in the bay is decreasing at a rate of 30 fish per day</u>.
- (b) Over the interval 0 ≤ t ≤ 8 the absolute minimum number of fish in the bay is;<u> 1,000</u>.
- (c) The values of <em>t</em> at which the rate of change is decreasing is; <u>3 ≤ t ≤ 8</u>
- (d) The rate of change of the number of pelicans flying near is; P' = <u>10·(3·c² - 24·c + 45)</u>
Reasons:
The given function is; f(t) = 10·(t³ - 12·t² + 45·t + 100)
Where;
t = Number of days
0 ≤ t ≤ 8
(a) The derivative of the given function is presented as follows;
F'(t) = 10 × (3·t² - 2×12·t + 45) = 10·(3·t² - 24·t + 45)
Therefore;
F'(4) = 10 × (3 × 4² - 24 × 4 + 45) = -30
Therefore F'(4) = -30 means that on day 4, the <u>number of fish in the bay is decreasing at 30 fish per day</u>.
(b) The absolute minimum is given as follows;
At a minimum or maximum value, F'(t) = 10·(3·t² - 24·t + 45) = 0
Which gives;
3·(t - 5)·(t - 3) = 0
t = 5, or t = 3
At t = 5, we have;
f(5) = 10 × (5³ - 12 × 5² + 45 × 5 + 100) = 1,500
At t = 3, we have;
f(3) = 10 × (3³ - 12 × 3² + 45 × 3 + 100) = 1,540
Therefore, f(5) = 1,500 is a local maximum
However, at x = 0, we have;
f(0) = 10 × (0³ - 12 × 0² + 45 × 0 + 100) = 1000
At x = 8, we have;
f(8) = 10 × (8³ - 12 × 8² + 45 × 8 + 100) = 2,040
Therefore, the absolute minimum is given at t = 8, where f(t) = <u>1,000</u>
(c) The values of <em>t</em> at which the rate of change in the number of fish in the
bay is decreasing is between the local maximum at t = 3, and the local
minimum at t = 5, which gives;
The rate of change of the number of fish is decreasing for values of t in the range;
- <u>3 ≤ t ≤ 5</u>
(d) P = 10·(t³ - 12·t² + 45·t + 100)
P' = 10·(3·t² - 24·t + 45)
At time t = c, we have;
- P' = 10·(3·c² - 24·c + 45)
<em>Based on a similar question online, we have;</em>
<em>(c) The interval over which the rate of change is decreasing</em>
<em>(d) The rate of change of the number of pelicans flying near the bay at t = c</em>
Learn more about differentiation of functions here:
Answer:
The amount invested at 3% is 300 &
The amount invested at 2% is 100.
Step-by-step explanation:
Total yearly interest for the two accounts is: $11
Let x be the amount invested at 3%
& y be the amount invested at 2%
From the question we can get 2 equations as;
x = 3y --------------------------Equation 1
0.03x + 0.02y = 11 ----------Equation 2
Substitute for x in Equation 2 we get;
0.03 (3y) + 0.02y = 11
0.09y + 0.02y = 11
0.11y = 11
Divide the above equation by 0.11, we get;
y =
y = 100
Let us substitute the value of y in Equation 1 we get;
x = 3(100)
x = 300
Now to check our answer let us put in the simple interest formula. If we get the sum of the two interests equal to 11 then our answers are correct:
0.03 x 300 + 0.02 x 100
= 9 + 2
= 11
Hence the amount invested at 3% is 300 and the amount invested at 2% is 100.