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. Part A 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. Part B 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. Part C Does the problem situation represent exponential growth or decay? Justify your reasoning.
Respuestas
Respuesta:
i think its this
Explicación paso a paso: Well, first thing I'd look for if there is a pattern in the sequence, and in this case there is multiplying by three every day. But, they've asked for a representation in exponential function model so that I'll give-the formula A(1) x r^n-1 is what we'll use to solve this problem. So the a stands for the first number in the sequence, so 5; then r with represent pattern within the sequence so 3; and n which is 5; so finally we have an equation 5 x 3^5-1 which when we use our calculator we get 405. A(1) was the first number in the sequence, R was pattern, and N was the number of elapsed days. On Friday there'd be 405 ants because we used our calculator. Growth, because the r isn't less than one.