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Andreyy89
3 years ago
7

Suppose f is a function with exponential growth and f(0)=1. Explain why f can be represented by a formula of the form

Mathematics
2 answers:
galben [10]3 years ago
7 0

We are supposed to explain why the given function can be expressed in form f(x)=b^{x}, when f(0)=1.

Since the given function is an exponential function we can express it as  f(x)=a(b)^{x}.

Now let us substitute x=0 in the given function,  

f(x)=b^{x}

f(0)=b^{0}  

f(0)=1  

Let us substitute x=0 in our function.    

f(0) = a(b)^{0}    

f(0) = a\cdot 1                    

f(0)=a  

Upon substituting a=1 in our function we will get,

f(x) = 1(b)^{x}

f(x) =(b)^{x}

Therefore, our function f can be represented by the formula of the form f(x)=b^{x}.

Firdavs [7]3 years ago
6 0

Answer: Because, here the rate of change is directly  proportional to the value of f(x) and it is satisfying the condition f(0)=1.

Explanation:

Since, Given function= f(x)= b^x, where b>1

let b=1+n where n is any positive number.

Thus, f(x)=(1+n)^x is an exponential function.( because its value is raising by the power of a constant 1+n )

And, for x=0, f(0)=(1+n)^0⇒f(0)=1

let n=1,  f(x) =2^x after making its graph we found that the function is growing and growth rate is positive.

Similarly, function f will be growing exponential for the every value of n. where f(0)=1.



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The sum of two numbers is 19. Three times the larger is 3 more than 6 times the smaller. Find the numbers.
ella [17]

Answer:

x=6

y=13

Step-by-step explanation:

The statement says that:

3x=6y+3\\

Been y the smaller and x the larger. The other equation that we have is the summation of the two numbers. Then we have 2 equations and 2  unknowns

1. 3x=6y+3\\2. x+y=19\\

Solving the equations the answers is x=13 and y=6.

6 0
2 years ago
Find the volume in cubic millimeters.
forsale [732]

Answer:

Option B is correct.

volume in cubic millimeters is, 8000 cubic mm

Step-by-step explanation:

Volume of a cube is found by multiplying the length of any edge by itself twice.

It is given by:

V = a^3 cubic units,......[1] where V represents the volume of a cube and a represents the side of a length.

From the given figure;

Length of a side(a) = 2 cm

Use conversion, to convert cm into mm;

1 cm = 10 mm

then;

2cm  =20 mm

⇒length of a side(a) = 20 mm

Substitute the value of a = 20 mm in [1];

V = (20)^3 cubic mm

Simplify:

V = 8000 mm^3

Therefore, the volume in cubic millimeters is, 8000 cubic mm


8 0
3 years ago
Read 2 more answers
Two intelligent, honest students are sitting together at lunch one day when their math teacher hands them each a card. “your car
Lady bird [3.3K]
Answer: The loser's card shows 6.

Explanation: Let's start by naming the first student A and the second student B.
Since the product of A and B are either 12, 15, or 18, let's list every single possibility, the first number being A's number and the second number being B's number.

1     12
1     15
1     18
2     6
2     9
3     4
3     5
3     6
4     3
5     3
6     2
6     3
9     2
12  1
15  1
18  1

Now, the information says that A doesn't know what B has, so we can immediately cross off all of the combinations that have the integer appearing once and once ONLY off, because if it happened once only, A would know of it straight away. Now, our sample space becomes much smaller.

1     12
1     15
1     18
2     6
2     9
3     4
3     5
3     6
6     2
6     3

Using this same logic, we know that we can cross off all of the digits that occur only once in B's column.

2     6
3     6

Now, A definitely knows what number B has because there is only one number left in B. Hence, we can conclude that the loser, B, has the integer 6.
4 0
3 years ago
GIVING BRAINLEST!!!Joe and Tim observed two points, P and Q, on a number line. A number line is shown from negative 1 to positiv
Veronika [31]

Answer:

Step-by-step explanation:

P is 5 ticks to the left of 0, so it would be -5/8

Q is 5 ticks to the right of 0, so it would be at 5/8

 an absolute value turns a negative number into a positive number

 so absolute value of  P located at -5/8 = 5/8

 this is the location of point Q

Joe said that the absolute values of the numbers represented by the two points are the same. 

8 0
3 years ago
Please help! I’ll give brainliest!
Jlenok [28]

Answer:

27 degrees withI think angle sum postulate

Step-by-step explanation:

6 0
2 years ago
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