Algebra 1 Unit 7: Exponential Functions Name______
Exponential Data - Growth date______block______
1) World Population Growth The current world population is 7.08 billion people (7,800,000,000). The population has been increasing at a steady percentage rate since the year 1950. The table below shows the world population every decade through 2000.
Calendar Year / Year since 1950 / World Population in billions1950 / 0 / 2.25
1960 / 10 / 2.71
1970 / 20 / 3.26
1980 / 30 / 3.92
1990 / 40 / 4.69
2000 / 50 / 5.64
a) Input the data in your graphing calculator or use desmos
b) Graph the data.
c) Calculate the regression equation and create your exponential function equation (rounding to thousandth, 3 decimal places)
d) Draw a rough sketch of your graph here – label the y-intercept with an ordered pair.
e) Interpolate data using the equation – what was the population in 1965?
f) Extrapolate data using the equation – what will the population be in 2020?
g) When will the population be 10 billioni?
2) Carbon Dating Scientists can determine the age of fossils they find by using a process called radio-carbon dating. An isotope called Carbon-14 decays by a regular percentage every year. Let’s say we’re doing an Archaeological dig in Egypt, and we find a mummified cat. It originally had 5 grams of carbon-14. We know the cat was buried 5000 years ago. Let’s call when it was buried “year 0”. The amount of carbon-14 for years since it was buried was calculated and presented in a table:
Years since mummified cat was buried / Amount of Carbon-14 (grams)0 / 5
100 / 1.495
200 / 0.447
300 / 0.133
400 / 0.039
h) Input the data in your graphing calculator or use desmos
i) Graph the data.
j) Calculate the regression equation and create your exponential function equation (rounding to thousandth, 3 decimal places)
k) Draw a rough sketch of your graph here – label the y-intercept with an ordered pair.
l) Interpolate data using the equation – How much carbon-14 was in the mummified cat 250 years after it was buried?
m) Extrapolate data using the equation – How much carbon-14 is in the mummy today (5000 years after it was buried)? Write your result in scientific notation.
n) When is the amount of carbon 0.3 grams?