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2 years ago

Construct the exponential function that contains the points (0,2) and (3,54)

Mathematics

1 answer:

erma4kov [3.2K]2 years ago

8 0

The exponential function that passes through (0,2) and (3,54) is a growth function

The exponetial function is y = 2 * 3^x

<h3>How to construct the exponential function?</h3>

The points are given as:

(x,y) = (0,2) and (3,54)

An exponential function is represented as:

y = ab^x

Substitute the points in the equation

2 = ab^0 and 54 = ab^3

Solve 2 = ab^0

a = 2

Substitute 2 for a in 54 = ab^3

54 = 2b^3

Divide by 2

27 = b^3

Take the cube roots of both sides

b = 3

So, we have:

y = ab^x

This becomes

y = 2 * 3^x

Hence, the exponetial function is y = 2 * 3^x

Read more about exponential functions at:

brainly.com/question/24077767

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Can anyone help with this?

scZoUnD [109]

203/3.5=58mi/h
243/4.5=54mi/h
(58+54)/2=56mi/h
The answer in 56mi/h

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4 years ago

In Exercise, find the derivative of the function.<br> y = 3ex - xex

nevsk [136]

Answer:

the question is incomplete, the complete question is "find the derivative of the function $y=3e^{x}-xe^{x}$ "

answer: $\frac{dy}{dx}=(2-x)e^{x}$ .

Step-by-step explanation:

From the equation, $y=3e^{x}-xe^{x}$ , we approach the question using the differentiation of a product and differentiation of a sum simultaneously,

the differentiation of a sum is express as

f(x)=u(x)+v(x)+.....w(x) then

$\frac{df(x)}{dx}=\frac{du(x)}{dx}+\frac{dv(x)}{dx}+...\frac{dw(x)}{dx}.\\$

For the differentiation of a product we have

f(x)=u(x)v(x), then

$\frac{df(x)}{dx}=\frac{dv(x)}{dx}u(x)+\frac{du(x)}{dx}v(x)$

hence if we go by the formula we arrive at

for $y=3e^{x}$

let u(x)=3 hence du/dx=0 and

$v(x)=e^{x}$ and $\frac{dv(x)}{dx}=e^{x}$

hence $\frac{dy}{dx}=3e^{x}+0e^{x}\\\frac{dy}{dx}=3e^{x}---equation 1\\$

Also for $y=-xe^{x}\\\frac{dy}{dx}=-e^{x}-xe^{x}---equation 2$ .

if we add equation 1 and equation 2 we arrive at

$\frac{dy}{dx}=3e^{x}-e^{x}-xe^{x}\\\frac{dy}{dx}=(3-1-x)e^{x}\\\frac{dy}{dx}=(2-x)e^{x}$ .

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3 years ago

The sum of the digits of a certain two-digit number is 7. Reversing its digits increase the number by 9. What is the number?

Elis [28]

Let the two numbers be x and y.

According to your question;

x + y = 7
10y + x = 10x + y + 9

By equation 1 ; x = 7-y

Substituting the value of x ;

10y + ( 7 -y) = 10(7-y) + y + 9

9y + 7 = 70 -10y + y + 9

9y + 7 = 70 - 9y + 9

=> 18y = 70 -7 + 9
=> 18y = 72
=> y = 4

Substituting for x ;

x = 7 - y
=> x = 7 -4
=> x = 3

Thus, x = 3 and y = 4;
=> The number is 34.

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3 years ago

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