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schepotkina [342]
3 years ago
14

1. Find an algebraic representation for an exponential function if it is known that f(x + 1) = 4.f(x)

Mathematics
1 answer:
MrMuchimi3 years ago
4 0

f(x)=4^{x-1} is the algebraic representation for an exponential function

Step-by-step explanation:

Given:

f(x + 1) = 4.f(x)

f(3) = 16

To Find:

Algebraic representation for an exponential function=?

Solution:

From the formula f(x+n) = 4^n f(x)

when n= 1, x= 3

f(3+1)= 4(1)f(3)

f(4)= 4f(3)

Substituting the value of f(3)

f(4)= 4f(3)

f(4)= 4 x 16  

f(4)= 64

f(4)=4^2

f (5) = 4^2 x 16

f (5) = 4^2 x  4^2

f(5)= 4^4

Similarly,

F(6) = 4^5

Hence, f(x)=4^{x-1}

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Stephan places £950 in his bank account which pays 1.6% simple interest per year.
ella [17]

Answer:

A. He will earn £15.2 each year

B. After one year he will have £965.2 in his account

Step-by-step explanation:

Applying the simple interest formula

A = P (1 + rt)

A = final amount

P = initial principal balance

r = annual interest rate

t = time (in years

Given data

Principal p= £950

Rate r= 1.6% =1.6/100= 0.016

Time t= 1 year

Substituting in our simple interest formula we have

A= 950(1+0.016*1)

A= 950(1+0.016)

A= 950(1.016)

A= £965.2

Interest = final amount - principal

= 965.2-950

= £15.2

8 0
3 years ago
Find (4.54×10^8)-(3.98×10^8)
horrorfan [7]

Answer:

5.6 *10^7

Step-by-step explanation:

Given

(4.54*10^8)-(3.98*10^8)

Required

Solve

(4.54*10^8)-(3.98*10^8)

Apply distributive law of algebra

(4.54 - 3.98) *10^8

Evaluate the expression in bracket

(0.56) *10^8

Remove bracket

0.56 *10^8

When a number is in standard form: a * 10^n

The value of a must be: 1 \le a \le 10

So, the expression becomes:

5.6 *10^{-1}*10^8

Apply law of indices

5.6 *10^{-1+8}

5.6 *10^7

5 0
2 years ago
In each of the following examples, a consumer purchases just two goods: x and y. Based on the information in each of the followi
SOVA2 [1]

The question is:

In each of the following examples, a consumer purchases just two goods: x and y. Based on the information in each of the following parts, sketch a plausible set of indifference curves (that is, draw at least two curves on a set of labeled axes, and indicate the direction of higher utility). Also, writedown a utility function u(x, y) consistent with your graph. Note that although all these preferences should be assumed to be complete and transitive (as required for utility representation), not all will be monotone.

(a) Jessica enjoys bagels x and coffee y, and consuming more of one makes consuming the other more enjoyable.

(b) Plamen loves mocha swirl ice cream x, but he hates mushrooms y.

(c) Jennifer likes Cheerios x, and neither likes nor dislikes Frosted Flakes y.

(d) Edward always buys three white tank tops x for every pair of jeans y.

(e) Nancy likes both peanut butter x and jelly y, and always gets the same additional satisfaction from an ounce of peanut butter as she does from two ounces of jelly.

Step-by-step explanation:

The utility functions consistent with the graphs are:

(a) u(x, y) = xy

(b) u(x, y) = x - y

(c) u(x, y) = x

(d) u(x, y) = min(x, 3y)

See attachments for the graphs.

8 0
2 years ago
Find the length of the missing side, rounded to the nearest-tenth.<br> 11<br> 9
KatRina [158]

Answer:

11=10 9 =10 because 5 or more is bring the number up but 4 or lest it rest

8 0
3 years ago
Which statement describes the graph of the system of equations below?
insens350 [35]
1.5x + 0.2y = 2.68....multiply by 0.3
1.6x + 0.3y = 2.98...multiply by - 0.2
------------------------
0.45x + 0.06y = 0.804 (result of multiplying by 0.3)
- 0.32x - 0.06y = - 0.596 (result of multiplying by - 0.2)
----------------------add
0.13x = 0.208
x = 0.208/0.13
x = 1.6

1.5x + 0.2y = 2.68
1.5(1.6) + 0.2y = 2.68
2.4 + 0.2y = 2.68
0.2y = 2.68 - 2.4
0.2y = 0.28
y = 0.28/0.2
y = 1.4

solution (they intersect at) (1.6,1.4)
8 0
3 years ago
Read 2 more answers
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