Final answer:
To find the equation of the tangent line to the curve y=2ˣ at the point (0,1), take the derivative of the function y=2ˣ, substitute x=0 to find the slope, and then write the equation of the line using the point-slope form.
Step-by-step explanation:
To find the equation of the tangent line to the curve y=2ˣ at the point (0,1), we need to find the slope of the tangent line first. The slope of the curve at any point can be found by taking the derivative of the function. In this case, the derivative of y=2ˣ is dy/dx = 2ˣ⋅ln(2). Since we want the slope at the point (0,1), we substitute x=0 into the derivative to get the slope m = 2ˣ⋅ln(2) = 2ˣ⋅0 = 0. Hence, the equation of the tangent line is y = mx + b, where m = 0. Substituting the point (0,1) into the equation, we find b = 1. Therefore, the equation of the tangent line is y = 0x + 1, which simplifies to y = 1.