G A sailing ship stopped at several islands, releasing one mating pair of goats onto each one. On the large island, the goats' growth rate was approximately exponential for a long time. If their per capita growth rate is 0.5 per year, how many years will it take before the goat population reaches 1000

12.4 years  

Step-by-step explanation:

Let recall the following,

The number of goats after t years is shown below

N = N₀∧ebt

Let N₀ = the number of the initial goats

b = The capital rate of growth

From the example given,

Let insert the values

N₀ is = 2

b = 0.5

Let N = 1000

So,

1000= 2e∧0.5t

e∧0.5t = 500

0.5t = ln 500 = 6.214

Therefore

t = 6.214/0.5 =12.4

Therefore, the number of years it will take for the goat population to reach 1000 is = 12.4 years  

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

the answer is 489

step-by-step explanation: