Thread: 2^(3.2)

Estimate 2^(3.2) to tenths without using a calculator and I need to show my arithmetic.

Sadieann

If you use the tangent line approximation

f(x+dx) = f(x)+f ' (x) dx

f(3+.2) = 2^3 + ln(2)*2^3*.2 = 9.11 exact 2^3.2 = 9.19

I don't see how to do this completely without a calulator unless you know ln(2) is .693 and you multiply by hand but that seems silly