Consider the initial value problem \displaystyle{\frac{dy}{dt} = \frac{1}{2}(y+1)} , where y(0)=0 .

Use the differential equation to find the slope of the tangent line to the solution curve

Slope =

Use the given initial value to find the equation of the tangent line to the solution curve at

Use the equation of the tangent line that you just found to approximate

Assuming that your approximation for

Slope =

Use the slope that you just found to find an approximate equation of the tangent line to the solution curve at

Use the equation of the tangent line that you just found to approximate

You can earn partial credit on this problem.