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vladimir1956 [14]
3 years ago
10

Model the data using an exponential function f(x) = Abx. HINT [See Example 1.]

Mathematics
1 answer:
zlopas [31]3 years ago
4 0
We take the function as a sequence

Term 1 ⇒ 5 
Term 2 ⇒ 4
Term 3 ⇒ 3.2

Between terms, there is a common ratio of ⁴/₅
We get it from here:
Term 2 / Term 1 = \frac{4}{5}
Term 3 / Term 2 = \frac{3.2}{4} = \frac{4}{5}

When a sequence has a common ratio between term, the sequence is a Geometric Sequence

n_{th}term=ar^{n-1}
Where a is the first term, r is the common ratio, and n is the term number

We have: a=5 and r= \frac{4}{5}
The formula for the function is

f(x)=5( \frac{4}{5})^{x-1}


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Read 2 more answers
What is the value of h when the function is converted to vertex form?
Dmitrij [34]

Answer:  The value of 'h' is 3.

Step-by-step explanation:  Given that the vertex form of a function is given by

g(x)=a(x-h)^2+k~~~~~~~~~~~~~~~~~~~~~~~~(i)

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g(x)=x^2-6x+14~~~~~~~~~~~~~~~~~~~~~~(ii)

From equation (ii), we have

g(x)=x^2-6x+14\\\\\Rightarrow g(x)=x^2-2\times x\times 3+3^2-3^2+14\\\\\Rightarrow g(x)=(x-3)^2-9+14\\\\\Rightarrow G(x)=(x-3)^2+5.

Comparing it with the vertex form (i), we get

h=3.

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