a) To find where the curve crosses the y-axis, we need to set x=0 in the equation:
y = e^(0.5x+3)
y = e^(0.5(0)+3)
y = e^3
Therefore, the curve crosses the y-axis at the point (0, e^3).
b) We are given that the curve passes through the point (-2, k). To find the value of k, we substitute x=-2 and solve for y:
y = e^(0.5x+3)
y = e^(0.5(-2)+3)
y = e^(2)
So the curve passes through the point (-2, e^2). Therefore, k = e^2.
c) We are given that the curve passes through the point (h, 100). To find the value of h, we substitute y=100 and solve for x:
y = e^(0.5x+3)
100 = e^(0.5x+3)
ln(100) = 0.5x+3
ln(100) - 3 = 0.5x
x = 2ln(10) - 6
Therefore, the curve passes through the point (2ln(10) - 6, 100). Hence, h = 2ln(10) - 6.