CPhill

I think that you mean :

f(x)  = ln (x^4)  = 4lnx

So

f ' (x) =    4/x

And

f ' ( e^3)  =

4 / (e^3)  =   about  0.199

8.35 ( 1 + .075)  =  about $8.98

8 3/4   =  35/4

3 1/2 =  7/2

So

(35/4) / (7/2)   invert the second fraction and multiply

(35/4) * (2/7)  =   swap denominators

(35/7) * ( 2/4)  =

5 * (1/2)  =

5/2   or  2.5   [as Rarinstraw said]

The amount remaining =

A₀(0.5)^(30000/5730)=

A₀ * (0.0265)  =   

About 3%

A is correct

Rarinstraw, MathEevee, Shane and guest  are correct......

The slope of the line = 5/2  =  gallons / minute  = 2.5

Answer  C

Spawn....I think the  annual growth rate  = 1.006^12  = about 7.4%

So....after 20 years, assuming that we want to use th annual growth rate formula, we have

10000 (1 + .074)^20  = about  $41,695  = $42000 [rounded per instructions]

And...as you point out.....C   is correct

Nice, Spawn!!!!

Very nice, Alan !!!!!!

C  is correct