Find the exponential model that fits the points shown in the graph. (Round the exponent to four decimal places)

Ramsey

Ramsey

Answered question

2020-11-07

Find the exponential model that best fits the graph's points. Exponent should be rounded to four decimal places.

Answer & Explanation

Liyana Mansell

Liyana Mansell

Skilled2020-11-08Added 97 answers

Given points on the exponential model: (0,1) and (5,16).
General equation of an exponential model: y=aebx
Evaluate the general equation at x=0 and x=5:
y=aeb(0)=ae0=a(1)=a
y=aeb(5)=ae5b
We require y=1 when x=0 and y=16 when x=5 (as the points (0,1) and (5,16) need to lie on the exponential model).
a=1
ae5b=16
By the first equation, we thus know that a=1. Let us replace ae5b=16 by 1 in the second equation:
e5b=16
Take the natural logarithm from each side of the previous equation (also using that the natural logarithm is the inverse of the exponential).
5b=ln16
Let us use the power property of logarithms (lna^b=blna) along with 16=24:
5b=4ln2
Divide each side of the previous equation by 5:
b=4ln25
Replacing a by 1 and b by 4ln25 in the general equation of the exponential model, we then obtain:
y=e4ln25x

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