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3 years ago

Explain why the initial value of any function of the formf(x) = a(b) is equal to a.

Mathematics

1 answer:

Fynjy0 [20]3 years ago

4 0

Answer:

The answer in the procedure

Step-by-step explanation:

we have

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

This is a exponential function

where

a is the initial value

b is the base

we know that

The initial value of the function is the value of f(x) when the value of x is equal to zero

substitute x=0 in the function

$f(0)=a(b)^{0}$

Remember that any number to the zero power is one

$(b)^{0}=1$

substitute

$f(0)=a*1=a$

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The system of equation used to find the Total number of flash cards made are $\left \{ {{5x+5} \atop {6x}} \right.$ .

In 5 minutes, each student will have 30 flash cards.

Step-by-step explanation:

Given:

Number of flash cards already made by Tristan = 5

Number of flash card Tristan makes in 1 min = 5

Number of flash card Josh makes in 1 min = 6

We need to find the How long will Josh have same number of flashcards.

Also We need to find how many flashcards will each student have at that point.

Solution:

Let the number of minutes be $'x'$ .

Now we can say that;

Total number of flash cards made by Tristan is equal to Number of flash cards already made by Tristan plus Number of flash card Tristan makes in 1 min multiplied by number of minutes.

framing in equation form we get;

Total number of flash cards made by Tristan = $5+5x$

Also We can say that;

Total number of flash cards made by Josh is equal Number of flash card Josh makes in 1 min multiplied by number of minutes.

framing in equation form we get;

Total number of flash cards made by Josh = $6x$

Hence the system of equation used to find the Total number of flash cards made are $\left \{ {{5x+5} \atop {6x}} \right.$ .

Now to find the number of minutes when both would have same number of flash cards we will make both the equation equal.

so we get;

$5+5x=6x$

On solving we get;

Combining like terms we get;

$6x-5x=5\\\\x=5\ mins$

Hence It would take 5 minutes when both will have same number of flash cards.

To find the number of flash cards each would had at that time we will substitute value of $x=5$ in the system of equations.

so we get;

number of flash cards made by Tristan = $5x+5 = 5\times5+5=25+5=30$

number of flash cards made by Josh = $6x =6\times 5 =30$

Hence In 5 minutes, each student will have 30 flash cards.

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3 years ago

Explain why the initial value of any function of the formf(x) = a(b) is equal to a.​

Explain why the initial value of any function of the formf(x) = a(b) is equal to a.