Help me!! please

Question

By analyzing available empirical data it was determined that during an illness a patient's body temperature fluctuated during one 24-hour period according to the function:

 

 

T(t)=0.0003(t-24)³ +101.70

 

where T represents that patient's temperature in degrees Fahrenheit and t represents the time of day in hours measured from 12:00 Am. Find the time as a function of temperature that is, the inverse function t(T) and the time (at nearest hour), was the patient's temperature 99.5°F.

 

Answer 1

To solve for t, first step is to subtract the 101.7 from each side and then make the necessary algebraic steps to isolate the t. 

 

T-101.7=.0003(t-24)³

Now divide both sides by .0003 to get

 

(T-101.7)/.0003=(t-24)³

now take the cubed root of both sides

 

[(T-101.7)/.0003]^1/3=t-24

finally add 25 to both sides to come up w your answer.

 

t=24+[(T-101.7)/.0003]^1/3 

substituting in 99.5 for T we have

t=24+[(99.5-101.7)/.0003]^1/3

t=24-19.43

=4.57

to the nearest hour would be 5 hours so 5am

Answer 2

To find the inverse function, you need to solve the function for t.

 

Start by subtracting 101.70 from both sides:

 

T - 101.70 = 0.0003 (t - 24)³

 

Next, divide both sides by 0.0003:

 

(T - 101.70)/0.0003 = (t - 24)³

 

Then, take the cubic root of both sides:

 

[(T - 101.70)/0.0003]^1/3 = t - 24

 

Finally, add 24 to both sides:

 

t = [(T - 101.70)/0.0003]^1/3 + 24

 

For the 2nd part, solve for t when T=99.5:

 

t = [(99.5 - 101.70)/0.0003]^1/3 + 24

t = 4.57 h

 

To the nearest hour, then, the patient's temp was 99.5 at 5 am.