What is this number in expanded form 29.601

There are several varieties of "expanded form." Pick the one that suits you.

29.601 = 20 + 9 + 0.6 + 0.00 + 0.001

29.601 = 2×10 + 9×1 + 6×.1 + 0×.01 + 1×.001

29.601 = 2×10¹ +9×10⁰ +6×10⁻¹ +0×10⁻² +1×10⁻³

I like the last form because it shows the nature of the place value system: each place represents some power of the number base. Here, the number is base-10. In other number bases, the 10 is replaced by the base value. In base-6, for example, the place value multipliers would be 6¹, 6⁰, 6⁻¹ and so on. (Of course the highest digit you would see in a base-6 number would be 5.) Once you understand this, you can do base conversions and arithmetic in any number base as easily as in base 10.

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50