How do you translate a word problem into an exponential equation?

Question

Suppose you have the question:

Daniel volunteered 2.5 hours in the library the first day and then the time he volunteered each day after increased by a factor of 2.4.

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Answer 1 · 2017-07-20T02:39:38

#H(d) = 2.5xx2.4^(d-1)#
Where #H(d)# represents the number of hours #(H)# volunteered on day #(d)#

With the symbol definitions above:

Day 1: #H(1) = 2.5#

Day 2:#H(2) = 2.5 xx 2.4^1#

Day 3:#H(3) = 2.5 xx 2.4^2#

Hence, in general, #H(d) = 2.5xx2.4^(d-1)#

NB: This becomes impossible after day 3 as the number of hours exceeds 24!