1. Find the derivative of the following functions using the
f(x+h) - f(x) h
a. ƒ(x) =
1 Show all your steps
2x .
Just remember its not (1/2)x. It should be 1/(2x)
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2. A rocket is fired into the air with an initial velocity of 98 m/s. The height ( h ) of the rocket after t seconds is given by the expression h = 98t - 4.9t2.
a. What the average rate of change for the first 2 seconds.
Time Height
0 0
1 93.1
2 176.1
Average rate of change = 88.2 m
I know the answer is 88.2. But can anyone please show me the steps thnx.
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3. If you invest $5000 compounded continuously at 4% p.a. how much will this investment be worth in 5 years?
you should use the formula A(t) = Pe^(rt)
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4. A population of 500 E. coli bacteria doubles every 15 minutes. Use this information to find an expression for this population growth. Using this expression, find what the population would be in 87 minutes. Use an exponential model.
In P(t) = 500 e^kt
for minutes, then:
1000 = 500 e^15k
2 = e^15k
15k = ln2
k = (ln2)/15
Now, I am stuck.
Now, can someone use the formula A(t) = Poe^(kt), and sub in what you know and sub in 87 for t to find A(t).
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5. c. What is the equation for the derivative of y = (0.75)x?
I GOT THIS y = 1.00000022063(0.75)x
I have 1.000(0.75)^x as an answer, but the 1.000.... is incorrect.. CAN SOMEONE FIX IT.
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6. Find the derivative of the following functions using the
f(x+h) - f(x) Show all your steps
h
a. ƒ(x) = x^2 + 5x
b. ƒ(x)=
1 2^x
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