1) Which equation could be used to estimate the population of Oak City in 10 years?
A) y = 48000(1.024)10
B) y = 48000(0.024)10
C) y = 48000(1.24)10
D) y = 48000(10.24)10

2) Which equation could be used to estimate Johnson City's population in 5 years?
A) y = 82000(1.983)5
B) y = 82000(0.983)5
C) y = 82000(−0.017)5
D) y = 82000(98.3)5

Question

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Respuesta :

luisejr77 luisejr77 · Answer 1 · 2019-04-23T00:30:20+02:00

Answer:

1) A

2) B

Step-by-step explanation:

For this problem we use exponential growth formulas

[tex]y = y_0(1 + r) ^ t[/tex] if the population increases when t increases

[tex]y = y_0(1-r) ^ 2[/tex] If the population decreases when t increases

Where and is the population as a function of time, [tex]y_0[/tex] is the initial population, r is the growth rate, t is the time in years.

1) In this situation we have that [tex]y_0 = 48000[/tex], the growth is 2.4%, then [tex]r = 0.024[/tex] and [tex]t = 10[/tex] and the equation is:

[tex]y = 48000(1 + 0.024) ^ {10}[/tex]

[tex]y = 48000(1.024) ^ {10}[/tex] -------- Option A)

2) In this situation we have that [tex]y_0 = 82000[/tex], the decrease is 1.7%, then [tex]r = 0.017[/tex] and [tex]t = 5[/tex] and the equation is:

[tex]y = 82000(1-0.017) ^ 5[/tex]

[tex]y = 82000(0.983) ^ 5[/tex] -------- Option B)