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I need help with some questions i did questions 1-3 already

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1 Answer

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Solution:

Given the graph below:

3) Horizontal asymptote

The above graph is an exponential function expressed as


P(t)=a(b)^t\text{ ---- equation 1}

To evaluate the horizontal asymptote, we need to evaluate the values of a and b.

Thus,


\begin{gathered} From\text{ the graph, when t=0, P\lparen t\rparen =5} \\ Thus,\text{ substitute these valuaes into equation 1} \\ 5=a(b)^0 \\ 5=a*1 \\ \Rightarrow a=5 \\ \end{gathered}

Substitute the value of a into equation 1.

Thus, we have


P(t)=5(b)^t----\text{ equation 2}

Also,


\begin{gathered} when\text{ t=1, P\lparen t\rparen=10} \\ substitute\text{ these values into equation 2} \\ 10=5(b)^1 \\ \Rightarrow10=5b \\ divide\text{ both sides by the coefficient of b, which is 5.} \\ (10)/(5)=(5b)/(5) \\ \Rightarrow b=2 \end{gathered}

Substitute the value of b into equation 2.

Thus, the exponential function P(t) becomes


P(t)=5(2)^t----\text{ equation 3}

To evaluate the horizontal asymptote, we take the limit of the function P(t) as t tends to infinity (either positive or negative).

Thus, we have


\lim_(t\to-\infty)P(t)=\lim_(t\to-\infty)(5(2)^t)=0

Hence, the horizontal asymptote of the function is at


P(t)=0

4) Domain of the function:

The domain of the P(t) function is the set of input values for which the P(t) function is real and defined.

Thus, the domain of the function is


-\infty\:<p>5) <strong>Range of the function:</strong></p><p>The range of the function P(t) is the set of dependable values for which the function P(t) is defined.</p><p>Thus, the range of the function is</p>[tex]P(t)>0

6) y-intercept.

The y-intercept is evaluated to be the value of P(t) when t equals zero.

Thus, at the y-intercept,


x=0

Thus, from the exponential function P(t),


\begin{gathered} P(t)=5(2)^t \\ at\text{ the y-intercept, x=0} \\ P(t)=5(2)^0=5*1 \\ \Rightarrow P(t)=5 \end{gathered}

Hence, the y-intercept of the function is 5.

This implies that at the snake population was 5 at the year the Scientists started keeping tracks of the population.

7) Point on the graph when x equals 1.

From the graph, the point (x,y) is


(1,10)

This implies that at the end of the first year the snake population is 10.

8) The function is an exponential function expressed as


P(t)=5\cdot2^t

9) To fill the table shown below:

we substiyute the respective values of t into the function P(t)

I need help with some questions i did questions 1-3 already-example-1
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User Terry Low
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