Question

2. The amount of fertilizer in a landscaping company’s warehouse decreases at a rate of 3% per week. The amount of fertilizer in the warehouse was originally 78,000 cubic yards. What function models the amount of fertilizer in cubic yards left after w weeks?

Answer 1

Answer: f(w) = 78,000 (0.97)^w

Step by step explanation:

The amount of fertilizer in the landscaping company's warehouse decreases by 3% per week

So,

3% ------> .03

now we subtract .03 from 1 and we get .97

1 - .03 = .97

and the function would look like this:

f(w) = 78,000 (0.97)^w

I have uploaded a pic to make it a little clearer. Hope it helps :-)

God bless

Answer 2

To solve the problem we must know about Exponential function.

What is the Exponential function?

An exponential equation shows the decrement of something from the original value after every period of time such that the decrement is at a constant rate.

$y =x(1-r)^n$

where,

y is the value after t period of time at a decrement rate of r.

The function that models the amount of fertilizer in cubic yards left after w weeks is $A = 78000(0.97)^w$.

Given to us

• Rate of decrement of fertilizer = 3% =0.03%
• Amount of fertilizer = 78,000 cubic yards

Which Function?

Given that the fertilizer is decreasing at a rate of 3%, therefore, it will follow the function,

$A = P(1-r)^t$

where,

A is the amount of fertilizer left after t weeks,

P is the amount of fertilizer in the initial phase,

r is the rate of decrement.

Function that models the Amount of fertilizer

We know that rate of decrement of fertilizer is 0.03 and the amount of fertilizer, in the beginning, was 78,000 cubic yards.

Substituting the values we get,

$A = P(1-r)^w$

$A = 78,000(1-0.03)^w\\\\A = 78000(0.97)^w$

Hence, the function that models the amount of fertilizer in cubic yards left after w weeks is $A = 78000(0.97)^w$.

Learn more about Exponential function:

https://brainly.com/question/15352175