Mary noticed 5 ants in her pantry on Monday. On Tuesday she counted 15 ants in the pantry. On Wednesday she counted 45 ants in the pantry.
Determine an exponential function model to represent the number of ants in the pantry in terms of the number of elapsed days. Explain how you arrived at your model.
Using your exponential model predict how many ants would be in the pantry by Friday if the trend continues. Explain if your response is reasonable.
Does the problem situation represent exponential growth or decay? Justify your reasoning.
Respuestas
Respuesta:
every day Mary's ants multiply by 3 successively
Explicación paso a paso:
An exponential function model to represent the number of ants in the pantry in terms of the number of elapsed days is : f(x)= 5*3ˣ
The numbers of ants would be in the pantry by Friday if the trend continues is: 405 .
The problem situation represent exponential growth.
How Mary noticed 5 ants in her pantry on Monday, on Tuesday she counted 15 ants in the pantry y on Wednesday she counted 45 ants in the pantry, then the exponential function model to represent the number of ants in the pantry in terms of the number of elapsed days is : f(x)= 5*3ˣ; x = 0,1,2,3,4,5... ( Monday, Tuesday, Wednesday, Thursday , Friday ...) .
Using my exponential model predict the numbers of ants would be in the pantry by Friday if the trend continues is:
Friday : x = 4
F(4) = 5*3⁴ = 405 ants
The problem situation represent exponential growth because by replacing the number of days you get more ants.
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Part B: By Friday there is going to be 405 ants because you multiply the Thursday that is 135 and you multiply Friday which it gets to 405.
Part C: It represents growth because the ants are multiplying not subtracting, and because each day theres more and more ants.