1. Consider the function f (x) = x2 - 6x + 7. Find the following:
(i)The intervals where the function is increasing or decreasing
(ii) Is the function concave up or concave down
2. Find the slope , the vertical and the horizontal intercepts of g(x) = 7x-224 . 8
3. Find the equation of the line passing through (9, -7) and (-3, 10).
4. Is the following function concave up or down? ( Justify)
Table 1: A function f in terms of t
|
t
|
0
|
3
|
6
|
9
|
12
|
15
|
18
|
21
|
|
f(t)
|
1.1
|
2.1
|
3.2
|
4.5
|
5.9
|
7.6
|
9.7
|
11.5
|
5. A product costs $280 today, How much will the product cost if the price is reduced by: (i) $4 a day.
(ii) 5% a day.
6. Solve the following equation : 2 ln(x) = ln(27 - 6x)
7. Find a possible formula for the exponential function that passes through (0, 500) and (3, 2000).
. Write in the form P(t) = P0 at (i) P (t) = 15 e0.25t
(ii) P (t) = 2 e-0.5t
9. A cup of coffee contains 100mg of caffeine which leaves the body at a continuous rate of 17% per hour.
(i) Write a formula for the amount A(t)mg of caffeine in the body t-hours after drinking a cup of coffee.
(ii) Graph the function( with the help of your calculator) and estimate the half life of caffeine
(iii) Use the Logarithm rules to find the Half life of caffeine.