Suppose y varies directly as x², and y = 160 when x = 4. Find y when x = 6.
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All you have to do is plug in the given values into the given equation and evaluate.
The expression is,
But we have to analyze the problem carefully. This is a natural phenomenon that can be modelled by a decay function. The reason is that, after every hour we expect the medicine in the blood to keep reducing.
Therefore we use the decay function rather. This is given by,
where,
and
On substitution, we obtain;
Now, we take our calculators and look for the constant
,then type e raised to exponent of -1.4. If you are using a scientific or programmable calculator you will find this constant as a secondary function. Remember it is the base of the Natural logarithm.
If everything goes well, you should obtain;
This implies that,
Therefore after 10 hours 24.66 mg of the medicine will still remain in the system.
The expression is,
But we have to analyze the problem carefully. This is a natural phenomenon that can be modelled by a decay function. The reason is that, after every hour we expect the medicine in the blood to keep reducing.
Therefore we use the decay function rather. This is given by,
where,
and
On substitution, we obtain;
Now, we take our calculators and look for the constant
,then type e raised to exponent of -1.4. If you are using a scientific or programmable calculator you will find this constant as a secondary function. Remember it is the base of the Natural logarithm.
If everything goes well, you should obtain;
This implies that,
Therefore after 10 hours 24.66 mg of the medicine will still remain in the system.