Suppose f (x) = 100x2 - 5x thousand units areproduced, where x is the number of years after 2000.a. What is f (10)?b. How many units are produced in 2010, accordingto this function?

1. A colony of bacteria doubles in size every hour. Initially there are 32 bacteria in a dish that can contain 32768 bacteria. a) Write a function N(t) that tells how b) After how many hours is the dish full? many bacteria are in the bowl after t hours.

4. Determine if each of the following functions is exponential or not. If so, write the function in the form f(x) = ab" (showing ALL work in doing so) and list the values of a and b. If not, simply write “Not exponential". (a) f(x) = 30Vr8 (b) f(æ) = 7·(v2)* (b) f(x) = 3

Sketch the graph of the exponential function f(x) = 3* + 2. Write down the domain and range of f from the graph in the box given below: Insert your name and ID and upload the graph.

The amount of a substance remaining (in grams) is given by the functionP (t) = 1.9(.89)^t/2where t is in seconds. What is the half-life of this substance?A. 22.912 secondsB. 8.264 secondsC. 2.974 secondsD. 0.336 secondsE. 11.896 second

16. A graphing calculator was purchased for Po dollars in 2018. The value of the calculator P (in dollars) can be expressed as a function of t, the number of years since 2018. Write a formula for P if the value of the calculator decreases by 7% each year. (a) P(t) = Po(0.07) (b) P(t) = Po – (0.07) (c) P(t) = Po(0.93) (d) P(t) = Po(0.3) (e) P(t) = Po - (0.93)

Suppose the weight (in pounds) of a baby boy x months old, for his first 10 months can be approximated by the function. f(x)=1.6x+8.3. Find the predicted weight at the age of 3 months .

Let P = 28000 (1.04)* be the population of a town t years after the year 2000. Estimate in which year the population will reach 35429.

A radioactive material loses mass according to the exponential relation y = 170 n (3) 28 where y is measured in grams and n is the number of days. Determine the amount of material remaining after 29 days.

Element X is a radioactive isotope such that its mass decreases by 20% every year. Ifan experiment starts out with 730 grams of Element X, write a function to representthe mass of the sample after t years, where the monthly rate of change can be foundfrom a constant in the function. Round all coefficients in the function to four decimalplaces. Also, determine the percentage rate of change per month, to the nearesthundredth of a percent.