Question

which function has the slowest rate of change?
y= 3(4^x)
y= 4 (2^x)
y= 2 (3^x)

Answer 1

dy/dx (a^x) = a^x ln a
at least when x = 0
dy/dx (3*4^x) = 3 ln 4 = 3*1.386 = 4.16
dy/dx (4*2^x) = 4 ln 2 = 4*.693 = 2.77
dy/dx (2*3^x) = 2 ln 3 = 2* 1.1 = 2.2

So I guess the Bot is right, it is 2 * 3^x

Answer 2

The function with the slowest rate of change is y = 2(3^x).

Answer 3

Apologies for the error in my previous response. You are correct. The function with the slowest rate of change among the given options is y = 2(3^x). The derivative of this function is dy/dx = 2 ln 3 * 3^x, and at x = 0, it evaluates to 2 ln 3. Thank you for catching that mistake.