The function f describes the value of a sculpture after t years. The function g describes the value of a painting by the same artist after t years.

f (t) = 500 (1.2) ^t

g (t) = 380 (1.15) ^t

Find function h, such that h (t) = f (t) - g (t).

h (x) = 120 (1.05) ^t

h (t) = 880 (1.35) ^t

h (t) = 20[25 (1.2) ^t - 19 (1.15) ^t]

h (t) = 20[19 (1.2) ^t - 25 (1.15^t]

Question

Alexia Mercado

Mathematics

8 September, 06:41

The function f describes the value of a sculpture after t years. The function g describes the value of a painting by the same artist after t years.

f (t) = 500 (1.2) ^t

g (t) = 380 (1.15) ^t

Find function h, such that h (t) = f (t) - g (t).

h (x) = 120 (1.05) ^t

h (t) = 880 (1.35) ^t

h (t) = 20[25 (1.2) ^t - 19 (1.15) ^t]

h (t) = 20[19 (1.2) ^t - 25 (1.15^t]

+4

Answers (2)

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Rihanna Ayers · Answer 1

H (t) = ft) - g (t)

h (t) = 500 (1.2) ^t-380 (1.15) ^t

Getting out 20 common factor:

h (t) = 20[500 (1.2) ^t/20-380 (1.15) ^t/20]

h (t) = 20[25 (1.2) ^t-19 (1.15) ^t]

Answer: Third option: h (t) = 20[25 (1.2) ^t-19 (1.15) ^t]

Lukas Lester · Answer 2

H (t) = f (t) - g (t)

= 500 (1.2) ^t - 380 (1.15) ^t

Taking out the greatest common factor, which is 20:

= 20[ (25) (1.2) ^t - (19) (1.15) ^t]

This is the third choice.

Note that you cannot subtract the bases of the exponents, for example (1.2^t - 1.15^t) cannot be simplified into something like 0.05^t.