Continue to complete the tables and questions. One of remaining items may have i

Question

Continue to complete the tables and questions. One of remaining items may have inequalities.

11. Function: y=50(2.718)^0.5t

When a bunch of rabbits were set free in a residential area, the animals had no natural predators, and so the population grew rapidly, according to the eqution at the left.

a. compared to its original size, how many times greater was the pop of rabbits after 5 yers?
b. According to the equation, what would be the pop of the rabbits at t= 10 yrs? does the same scale factor apply?
c. For what interval of time will the number of rabbits exceed 30,000?

Table:

Time(yrs) Population (# rabbits)
t y
0
1
2
3
4
5

Explanation / Answer

we have

y=50(2.718)^0.5t

if t=0    y=50(2.718)^0.5(0) y=50

if t=1    y=50(2.718)^0.5(1) y=50(1,6486) y=82,43182

if t=2    y=50(2.718)^0.5(2) y=50(2,718) y=135,9136

if t=3    y=50(2.718)^0.5(3) y=50(4,4809) y=224,04224

if t=4    y=50(2.718)^0.5(4) y=50(7,3875) y=369,37369

if t=5    y=50(2.718)^0.5(5) y=50(12,179) y=608,96609

so

Time(yrs) Population (# rabbits)
t y
0 50
1 82
2 136
3 224
4 369
5 609

a) if t=5 y=608,96

608,96/5012,18 is the factor of increase

b) if t=10 y=50(2.718)^0.5(10) y=50(148,336) y=7416,817417

7416,81/50=148,336 does not apply the same factor

c) if y=30000

50(2.718)^0.5(t)=30000

2,718^0,5t=600

ln(2,718^0,5t)=ln600

0,5t*ln(2,718)=ln600 ln(2,718)1

t=ln600 /0,5

t12,79 years

in the interval where t exceed 12,79 years

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