In an experiment a persons body temperature is given by T=310-(7/9)^n where n is the number of minutes after in an experiment a persons body temperature is given by T=310-(7/9)^n where n is the number of minutes after the start of the experiment and T is the temperature in kelvin (K). what temperature does the body approach after a long time?
A. 310
B. 300
C. 305
D. 450
after a "long time" t --->∞
and (7/9)^t becomes smaller and smaller
eventually it will approach zero
so we are left with
T = 310 - 0 = 310
check:
test with t = 100
T = 310 - (7/9)^100
= 310 - 1.2177x10^-11
= 310 - 0 for all practical purposes
= 310
To find the temperature that the body approaches after a long time, we can observe the behavior of the equation T = 310 - (7/9)^n as n becomes very large.
In this equation, (7/9)^n represents a decreasing exponential term. As n increases, the value of (7/9)^n will get smaller and closer to zero. This is because when a value between 0 and 1 is raised to a power, it becomes smaller as the power increases.
Since the temperature T is subtracted by (7/9)^n, it will approach 310 as n becomes large. Therefore, the body temperature approaches 310 Kelvin (K).
So, the answer is A. 310