Consider the initial value problem    dy dt = y + t y(0) = 0 (7) (a) approximate y(0.5) using euler’s method with stepsize ∆t = 0.25. (b) approximate y(0.5) using euler’s method with stepsize ∆t = 0.1. (c) find the exact solution of the differential equation and use it to compute the exact value of y(0.5). are the approximations from parts (a) and (b) over-approximating or under-approximating the value of y(0.5)? explain why this occurs.

other answer is correct. i had used the radius of the radius somehow. a website:

f(x)=2/3x-8, which give g(x) the greatest value.

step-by-step explanation:

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places