An adult takes 500 milligrams (mg) of ibuprofen. Each hour, the amount of ibuprofen in the person's system decreases by one-fifth. Write the function that models the exponential change between the number of hours, t, and the number of milligrams of ibuprofen remaining in the person's system, m(t). Om(t) = 500-5t Om(t) = -500-5t Om(t)=500. °·(²)* Om(t)=-500- ·(²³)*

Engineers are draining a water reservoir until its depth is only 10 feet. The depth decreases exponentially as shown in the graph below. The engineers measure the depth adter 1  hour to be 64 feet and after 4 hours to be 28 feet. Develop an exponential equation in y=a(b)^2 to predict the depth as a function of hours draining. Round a to the nearest integer and b to the nearest hundredth. The, graph the horizontal line y = 10 and find its intersection to determine the time, to the nearest tenth of an hour, when will the reservoir reach a depth of 10 feet?

Fill in the table for the exponential function given by f (x) = 3 (2)" 0 1 C X -1 f(x) a a. -8 2 d type your answer... b. -4 C. type your answer... d.

A pair of​ women's running shoes cost ​$125 in 2008 and the same shoes cost ​$140 in 2012 due to inflation.   a. Develop an exponential model to describe the rate of inflation over this time period. form: y=125(___)x^2   b. If inflation continues at the same​ rate, use your model in part​ (a) to estimate the price of the shoes in 2018.

Need only a handwritten solution only (not a typed one).

The tuition at a public university was $21,000 in 2008. Between 2008 and 2010, the tuition had increased by 15%. Since then, it has continued to grow exponentially. Select all statements that describe the growth in tuition cost. А: The tuition cost can be defined by the function f (y) = 21, 000 · (1.15)3, where represents years since 2008. B: The tuition cost increased 7.5% each year. C: The tuition cost increased about 7.2% each year. D: The tuition cost roughly doubles in 10 years. E: The tuition cost can be approximated by the function f (d) = 21,000 - 24, where d represents decades since 2008.

The number of food trucks in a city has been increasing by 50% annually. There were two food trucks in the year 2010. A. Write an exponential growth function that represents the number of food trucks t years after 2010 B. How many food trucks will there be in the year 2030?

An investment earns 4% per year and is worth $10,000 after 7 years. PV =

A desalinization process is eliminating 20% of the salt from seawater every 10 minutes. There are initially 450 g of salt in 10 liters of water. Find an exponential function for A, the grams of salt in the 10 liters of seawater t minutes after the process has begun. A= ? Use the model to predict the amount of salt (in grams) in the seawater after 35 minutes. Round to the nearest whole number. Which is 206 g.

Let t be the number of years since 1989. What does t=6 mean in this situation