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2 years ago

Does the function f(x) = 7^x+ 3 represent exponential growth, decay, or neither?

1 answer:

5 0

D) the answers growth because when the number 7 (in that position) is raised to a power it will grow at the rate of 7 to the power of (x)

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If the diameter of the following circle is tripled, which of the following expressions could be used to find the area of the new

sashaice [31]

Answer:

9(254.34 in. 2)

and

7ft

Step-by-step explanation:

6 0

2 years ago

(a) Use a linear approximation to estimate f(0.9) and f(1.1). f(0.9) ≈ f(1.1) ≈ (b) Are your estimates in part (a) too large or

olasank [31]

Answer:

(Missing part of the question is attached)

$L(x)=2x+3$

Estimates are too large.

Step-by-step explanation:

Suppose the only information we know about the function is:

$f(1)=5$

where the graph of its derivative is shown in the attachment

If the function $f\\$ is differentiable at point $x=1$ , the tangent line to the graph of $f$ at 1 is given by the equation:

$y=f(1) +f'(1)(x-1)$

So we call the linear function:

$L(x)=f(1) +f'(1)(x-1)$

We know the $f(1)=5$ as it is given in the question, and $f'(1)=2$ from the graph attached. Substitute in the equation of $L(x)$ .

$L(x)=5+2(x-1)\\L(x)=5+2x-2\\L(x)=2x+3\\$

At x=1, $f'(x)$ is positive but it is decreasing. However. if we draw the tangent lines, we see that the tangent lines are becoming less steeper, so the tangent lines lie above the curve $f$ . Thus, The estimates are too large.

4 0

2 years ago

The sum of two terms of gp is 6 and that of first four terms is 15/2.Find the sum of first six terms.

Gnoma [55]

Given:

The sum of two terms of GP is 6 and that of first four terms is $\dfrac{15}{2}.$

To find:

The sum of first six terms.

Solution:

We have,

$S_2=6$

$S_4=\dfrac{15}{2}$

Sum of first n terms of a GP is

$S_n=\dfrac{a(1-r^n)}{1-r}$ ...(i)

Putting n=2, we get

$S_2=\dfrac{a(1-r^2)}{1-r}$

$6=\dfrac{a(1-r)(1+r)}{1-r}$

$6=a(1+r)$ ...(ii)

Putting n=4, we get

$S_4=\dfrac{a(1-r^4)}{1-r}$

$\dfrac{15}{2}=\dfrac{a(1-r^2)(1+r^2)}{1-r}$

$\dfrac{15}{2}=\dfrac{a(1+r)(1-r)(1+r^2)}{1-r}$

$\dfrac{15}{2}=6(1+r^2)$ (Using (ii))

Divide both sides by 6.

$\dfrac{15}{12}=(1+r^2)$

$\dfrac{5}{4}-1=r^2$

$\dfrac{5-4}{4}=r^2$

$\dfrac{1}{4}=r^2$

Taking square root on both sides, we get

$\pm \sqrt{\dfrac{1}{4}}=r$

$\pm \dfrac{1}{2}=r$

$\pm 0.5=r$

Case 1: If r is positive, then using (ii) we get

$6=a(1+0.5)$

$6=a(1.5)$

$\dfrac{6}{1.5}=a$

$4=a$

The sum of first 6 terms is

$S_6=\dfrac{4(1-(0.5)^6)}{(1-0.5)}$

$S_6=\dfrac{4(1-0.015625)}{0.5}$

$S_6=8(0.984375)$

$S_6=7.875$

Case 2: If r is negative, then using (ii) we get

$6=a(1-0.5)$

$6=a(0.5)$

$\dfrac{6}{0.5}=a$

$12=a$

The sum of first 6 terms is

$S_6=\dfrac{12(1-(-0.5)^6)}{(1+0.5)}$

$S_6=\dfrac{12(1-0.015625)}{1.5}$

$S_6=8(0.984375)$

$S_6=7.875$

Therefore, the sum of the first six terms is 7.875.

5 0

2 years ago

A movie theater sends out a coupon for 25% off the price of a ticket. Write an equation for the situation, where y is the pric

PilotLPTM [1.2K]

Answer:

Step-by-step explanation:

x-the original price

y- the discounted price

y= the original price - 25 % discounted from x = x- (.25*x) = x( 1-.25) = .75x

equation is y= .75x

The equation should only be in the first quadrant because the prices can only be positive numbers.

5 0

2 years ago

What is the solution of log2x+3125 = 3? (1 point)

enot [183]

Answer:

$x = - 1062.5$

Step-by-step explanation:

Assuming the equation is:

$log(2x + 3125) = 3$

Then taking antilogarithms gives:

$2x + 3125 = {10}^{3}$

We simplify on the left to get:

$2x + 3125 = 10 \times 10 \times 10$

This gives us:

$2x + 3125 =1000$

We subtract 3125 from both sides to get:

$2x = 1000 - 3125$

$2x = - 2125$

$x = - 1062.5$

6 0

2 years ago