Answer to Question #256959 in Calculus for junior

Question #256959
  1. A plant grows 1.67 cm in its first week. Each week it grows by 2% more than it did the week before. By how much does it grow in twenty weeks, including the first week?

2.  Two functions f and g are defined on the set R, of real numbers by

f:x-> 2x - 3 or f:x-> 2x-3/x

x

and

g : x -> 1- 3x OR g:x-> 1- 3x/2 Find the inverse of the function f and the domain of gof.

2


1
Expert's answer
2021-10-27T11:00:03-0400

1.The length of a plant each week form an geometric sequence with b1=1.67b{\scriptscriptstyle 1}=1.67 and q = 1.02

We have to find the sum of the first 20 elements of this sequence. The formula of the first n elements is:

Sn=b1(1qn)1qS{\scriptscriptstyle n}={\frac{b{\scriptscriptstyle 1}*(1-q^{n})} {1-q}}

In our case: S20=1.67(1.02201)1.021=124.07S{\scriptscriptstyle 20}={\frac{1.67*(1.02^{20}-1)} {1.02-1}} = 124.07 cm

2. f:x-> 2x - 3

f(x) = 2x-3. To find it inverse we should express x in terms of f(x): x=f(x)+32x={\frac{f(x)+3} 2}

The inverse of this function is f1:xx+32f^{-1}: x\to{\frac{x+3} 2}

x -> 1- 3x

(gof)(x) = 1-3(2x-3) = 1-6x+9. The domain of this function is x є R

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment