The exponential model a=58.7e^0.02t describes the population, a, of a country in millions, t years after 2003. use the model to determine when the population of the country will be 89 million.

About 20.81 years

Step-by-step explanation:

89 million is the "final population" -- population after t years.

So, 89 million would be in "A" in the equation. Then we will have to solve for "t" by taking LN (natural logarithm). That is how we solve exponential equations.

So,

Now we recognize the exponential rule of:

Ln(e) = 1

and we use the property:

Now, we solve by taking Ln of both sides:

So, population would be 89 million in about 20.81 years

answer: there are 453.592 grams in a pound.

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3