b.) State the domain and range of the function shown in your graph. c.) Indicate

Question

b.) State the domain and range of the function shown in your graph.

c.) Indicate the intervals on which f(x) is increasing, on which f(x) is decreasing, and on which f(x) is neither increasing nor decreasing. Mak sure your answers match your graph.

d.) Indicate the intervals on which f(x) is concave up, on which f(x) is concave down, and on which f(x) is neither concave up nor concave down. Make sure your answers match your graph.

2. Find a formula for the exponential function passing through the points (-2, 4/25) and (2,100).

3. A radioactive substance decays exponentially. A scientist beings with 120 milligrams of radioactive substance. After 32 hours, 60mg of the substance remains. How many milligrams will remain after 47 hours?

4. A population of bacteria is growing according to the equation P(t) = 1900e^0.1t. Estimate when the population wil exceed 2892.

Explanation / Answer

2. Find a formula for the exponential function passing through the points (-2, 4/25) and (2,100).

Lets write the formula as :

y = a(b)^x

Using (-2 , 4/25) :
4/25 = a(b)^-2

Using (2 , 100) :
100 = a(b)^2

Dividing those equations :
100 / (4/25) = ab^2/(ab^-2)

100*25/4 = b^4

5^4 = b^4

So, b = 5

And then we can find a :
100 = a(5)^2
a = 4

So, equation is :

y = 4(5)^x ----> ANSWER

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4)
P = 1900e^(0.1t)

2892 = 1900e^(0.1t)

2892/1900 = e^(0.1t)

e^(0.1t) = 1.5221052631578947

0.1t = ln(1.5221052631578947)

t = ln(1.5221052631578947) / 0.1

t = 4.2 approx -----> ANSWER

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