Core Math Investigation
1) When x is more than 0 and increases (e.g. from 5 to 6), y increases
at a much faster rate and becomes very big. When x increases when it
is less then 0 (e.g. from –10 to –9), y increases very slowly.
2) (i) The value of a affects the value of x proportionally. For
example we can compare the equations y = 1 + 2x and y = 5 + 2x. In the
second equation, the value of a has been change to 5. As we can see
from the results in Tables 1 and 2, all the values of y for y = 5 + 2x
are greater by 4, when x is the same.
(ii) As we have seen in (i), the effect of a does not affect the value
of y, as it is a constant added to the solution of 2x . Hence, the
value of a affects x proportionally, no matter what the value of x is.
3) (i) For b = -1, b causes the value of y decrease rapidly as x
increases. This is because when x becomes larger, bx will be a very
small number as bx will be small as b is negative while x is positive.
For b = 0, y remains constant throughout, no matter what the value of
x is. This is because 0x will always give 0. For b = 1, the
relationship is the same as in (1), as 1x will always lead to a rapid
rate of increase for y when x> 0.
(ii) For b = -1, b causes y to increase greatly when x gets smaller,
as b is a negative number and so bx will give a large number when both
b and x are negative. For b = 0, y remains constant throughout, no
matter what the value of x is. This is because 0x will always give 0.
For b = 1, the relationship is the same as in (1), as 1x will always
lead to a very slow rate of increase for y when x <0.
Step Three: The next step will involve getting the variable by itself, in this case ‘x’ is the variable. So, to get ‘x’ by its self we must subtract 100 from both sides.
B has increased by one fifth of what Test tube A is and Test tube C
Next, the constant multiple rule is the derivative of a constant times a function, is just the constant times the derivative and It states:
5. (Scenario: Growth Rates) Look at the scenario Growth Rates. According to the rule of
3. How small must the combination of F and X be to make this an
2. Take any two of the above and give two interpretations that explain away the difficulty.
0.6M has the greatest slope. Its equation was 0.128x + 9.62 which was greater compared to other values. The smallest was for 0.0M where we got the equation as 0.005x + 9.88 which is the smallest compared to other values. m is the change in mass over time therefore we can see greater change for 0.6M whereas smaller change for 0.0M. This is because osmosis was more favorable for 0.6M
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-In order to solve this differential equation you look at it till a solution occurs to you.
B. i ask that you should think about these precautions and take them into thought