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# Core 3 exponential help watch

1. Hey was just wondering if anyone could help me with the question

The temperature of a room (T) is controlled by a thermostat such that when the temperature falls to 12degrees the heater is turned on until the temperature reaches 18degrees. the room then cools until it reaches 12degrees again.
time (t) is in minutes

for t in the interval 10< t < 60

T = 5 + Ae^(-kt)

where A and K are constants
given that T=18 when t=10 and that T=12 when t=60

i) show that k = 0.0124 to 3 sig figs and find the value of A
ii) find the rate at which the temp of the room is decreasing when t=20

cheers for any help
2. Put the values in to the given formula and you'll have two equations, re-arrange both for A equals, make the two equations equal to each other (eliminating A) and you should be able to work it out from there.

ii) Is easy. Just think about it. What do you do to find the rate of change of any formula with respect to a certain variable?

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