exponential

Zombies are doubling every 2 days. If two people are turned into zombies today, how long will it take for the population of about 600,000 to turn into zombies? Let d = every 2 days. We set up the exponential equation 2 * 2^d = 600,000 Divide each side by 2: 2^d = 300000 To solve this equation...

Matthew's pay increases by 20% each month. If his first pay is $450, determine the amount of his pay in month 5. Let me be the number of months. We have a pay functionalists P(m) as: P(m) = Initial Pay * (1 + Increase %/100)^m With m = 5, initial pay = 450, and Increase % = 20, we have P(5) =...

The flu is starting to hit Lanberry. Currently, there are 894 people infected, and that number is growing at a rate of 5% per day. Overall, how many people will have gotten the flu in 5 days? Our exponential equation for the Flu at day (d) is: F(d) = Initial Flu cases * (1 + growth rate)^d...

Plutonium 241 has a decay rate of 4.8 % per year. How many years will it take a 50 kg sample to decay to 10 kg? Since 4.8% is 0.048, we have decay as: 50 * (1 - 0.048)^n = 10 0.952^n = 0.2 Typing this into our math engine, we get: n = 32.7186 years

A virus is spreading exponentially. The initial amount of people infected is 40 and is increasing at a rate of 5% per day. How many people will be infected with the virus after 12 days? We have an exponential growth equation below V(d) where d is the amount of days, g is the growth percentage...

the university of california tuition in 1990 was $951 and tuition has been increasing by a rate of 26% each year, what is the exponential formula Let y be the number of years since 1990. We have the formula T(y): T(y) = 951 * 1.26^y

A car drives 3 feet the first second, 9 feet in the next second, and 27 feet in the third second. If the pattern stays the same, how far will the car have traveled after 5 seconds, in feet? Our pattern is found by the distance function D(t), where we have 3 to the power of the time (t) in...

If 200 bacteria triple every 1/2 hour, how much bacteria in 3 hours Set up the exponential function B(t) where t is the number of tripling times: B(d) = 200 * (3^t) 3 hours = 6 (1/2 hour) periods, so we have 6 tripling times. We want to know B(6): B(6) = 200 * (3^6) B(6) = 200 * 729 B(6) = 145,800

A private high school charges $36,400 for tuition, but this figure is expected to rise 10% per year. What will tuition be in 10 years? Let the tuition be T(y) where y is the number of years from now. We've got: T(y) = 36400 * (1.1)^y The problem asks for T(10) T(10) = 36400 * (1.1)^10 T(10) =...

A super deadly strain of bacteria is causing the zombie population to double every day. Currently, there are 25 zombies. After how many days will there be over 25,000 zombies? We set up our exponential function where n is the number of days after today: Z(n) = 25 * 2^n We want to know n where...

A city has a population of 240,000 people. Suppose that each year the population grows by 7.25%. What will the population be after 9 years? Let's build a population function P(t), where t is the number of years since right now. P(t) = 240,000(1.0725)^t <-- 7.25% as a decimal is 0.0725 The...

Scientists are studying a cell that divides in half every 15 minutes. How many cells will there by after 2.5 hours? Divide 2.5 hours into 15 minute blocks. 2.5 hours = 2(60) + 0.5(60) minutes 2.5 hours = 120 + 30 minutes 2.5 hours = 150 minutes Now determine the amount of 15 minute blocks 150...