A red-hot sword was plunged into cold water. This caused the temperature difference between the sword and the water to decrease rapidly.
The relationship between the elapsed time t, in seconds, since the sword was plunged into water, and the
temperature difference, D(t), is modeled by the following function:
t
9.7
D(t) = 256
4
Complete the following sentence about the decay rate of the temperature difference.
1
The temperature difference is reduced by a factor of
4
every
seconds.

2^y = ln 5, or   y(ln 2) = ln 5.   solving for y,   y = (ln 5) / (ln 2).   y=5

step-by-step explanation:

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, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

yes

step-by-step explanation:

yes