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3 years ago

Write a recursive and an explicit formula to represent the following sequence 52, 40, 28, 16,...

Mathematics

1 answer:

horrorfan [7]3 years ago

5 0

Answer:

Explicit tn = 52 + (n - 1)*(-12)

Recursive = tn = t(n - 1) - 12

Step-by-step explanation:

The difference between term n and term n - 1 is can be found by taking the difference between and 2 consecutive terms.

t3 = 28

t2 = 40

d = t3 - t2

d = 28 - 40

d = - 12

Explicit

tn = a1 + (n - 1)*d

a1 = 52

d = - 12

tn = 52 + (n - 1)*(-12)

Example

Find t5

t5 = 52 + (5 - 1)*(-12)

t5 = 52 + 4 * - 12

t5 = 52 - 48

t5 = 4

Recursive

tn = t(n - 1) - 12

Example

t5 = t4 - 12

t5 = 16 - 12

t5 = 4 just as it did before.

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lara31 [8.8K]

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8 0

3 years ago

Read 2 more answers

I dont understand how to do this precalc question

Alexeev081 [22]

Answer:

x-intercept: (-0.1, 0)
Horizontal Asymptote: y = -3
Exponential growth

(First answer option)

Step-by-step explanation:

General form of an exponential function

$y=ab^x+c$

where:

a is the initial value (y-intercept).
b is the base (growth/decay factor) in decimal form:
If b > 1 then it is an increasing function.
If 0 < b < 1 then it is a decreasing function.
y=c is the horizontal asymptote.
x is the independent variable.
y is the dependent variable.

Given exponential function:

$y=4(10)^x-3$

<h3>x-intercept</h3>

The x-intercept is the point at which the curve crosses the x-axis, so when y = 0. To find the x-intercept, substitute y = 0 into the given equation and solve for x:

$\begin{aligned}& \textsf{Set the function to zero}:& 4(10)^x-3 &=0\\\\& \textsf{Add 3 to both sides}:& 4(10)^x &=3\\\\& \textsf{Divide both sides by 4}:& 10^x &=\dfrac{3}{4}\\\\& \textsf{Take natural logs of both sides}:& \ln 10^x &=\ln\left(\dfrac{3}{4}\right)\\\\& \textsf{Apply the power log law}:&x \ln 10 &=\ln\left(\dfrac{3}{4}\right)\\\\& \textsf{Divide both sides by }\ln 10:&x&=\dfrac{\ln\left(\dfrac{3}{4}\right)}{\ln 10} \\\\& \textsf{Simplify}:&x&=-0.1\:\:\sf(1\:d.p.)\end{aligned}$