ex
Alyssa is an ecologist loses \dfrac{1}{18}181start fraction, 1, divided by, 18, end fraction of its size every 222 months. 185,000185, comma, 000 foxe
185000*(17/18)^t/2
After a special medicine is introduced into a petri dish full of bacteria, the number of bacteria remaining in the dish decreases rapidly. The relationship between the elapsed time ttt, in seconds, and the number of bacteria, B(t)B(t)B, left parenthesis, t, right parenthesis, in the petri dish is modeled by the following function: B(t)=9300⋅(164)t
1/2 every .17
Tobias sent a chain letter to his friends, asking them to forward the letter to more friends. The number of people who receive the email increases by a factor of 444 every 9.19.19, point, 1 weeks, and can be modeled by a function, PPP, which depends on the amount of time, ttt (in weeks). Tobias initially sent the chain letter to 37 friends.
37*(4)^t/9.1
Derek sent a chain letter to his friends, asking them to forward the letter to more friends. The group of people who receive the email gains \dfrac{9}{10}109start fraction, 9, divided by, 10, end fraction of its size every 333 weeks, and can be modeled by a function, PPP, which depends on the amount of time, ttt (in weeks). Derek initially sent the chain letter to 404040 friends.
40*(1.9)^t/3
After a special medicine is introduced into a petri dish containing a bacterial culture, the number of bacteria remaining in the dish decreases rapidly. The bacterial culture loses 25\%25%25, percent of its size every 141414 seconds, and can be modeled by a function, NNN, which depends on the amount of time, ttt (in seconds). Before the medicine was introduced, there were 45{,}00045,00045, comma, 000 bacteria in the Petri dish.
45000*(.75)^t/14
On the first day of spring, an entire field of flowering trees blossoms. The population of locusts consuming these flowers rapidly increases as the trees blossom. The locust population gains \dfrac{6}{7}76start fraction, 6, divided by, 7, end fraction of its size every 2.42.42, point, 4 days, and can be modeled by a function, LLL, which depends on the amount of time, ttt (in days). Before the first day of spring, there were 460046004600 locusts in the population.
4600*(13/7)^t/2.4
Nicholas sent a chain letter to his friends, asking them to forward the letter to more friends. Every 121212 weeks, the number of people who receive the email increases by an additional 99\%99%99, percent, and can be modeled by a function, PPP, which depends on the amount of time, ttt (in weeks). Nicholas initially sent the chain letter to 505050 friends.
50*(1.99)^t/12
After a special medicine is introduced into a petri dish containing a bacterial culture, the number of bacteria remaining in the dish decreases rapidly. The number of bacteria decays by a factor of \dfrac{1}{15}151start fraction, 1, divided by, 15, end fraction every 6.76.76, point, 7 minutes, and can be modeled by a function, NNN, which depends on the amount of time, ttt (in minutes). Before the medicine was introduced, there were 90{,}00090,00090, comma, 000 bacteria in the Petri dish.
90000*(1/15)^t/6.7
Ocean sunfish are well-known for rapidly gaining a lot of weight on a diet based on jellyfish. The relationship between the elapsed time, ttt, in days, since an ocean sunfish is born, and its mass, M(t)M(t)M, left parenthesis, t, right parenthesis, in milligrams, is modeled by the following function: M(t)=(1.34)t6+4
Every day, the mass of the sunfish is multiplied by a factor of 1.05
Elon sent a chain letter to his friends, asking them to forward the letter to more friends. The relationship between the elapsed time, ttt, in days, since Elon sent the email, and the total number of people who receive the email, P(t)P(t)P, left parenthesis, t, right parenthesis, is modeled by the following function: P(t)=4⋅3t
Every day, the number of people who receive the email grows by a factor of 3
Dominic sent a chain l Phour(t)=18⋅(1.05)t
Every day, the number of people who receive the email grows by a factor of 3.23.
On the first day of winter, an entire field of trees starts losing its flowers. N(t)=8950⋅(0.7)2t
Every day, there is a 51% percent removal from the locust population.
Gottfried wanted to see how contagious yawning can be. To better understand this, he conducted a social experiment by yawning in front of a random large crowd and observing how many people yawned as a result. The relationship between the elapsed time ttt, in minutes, since Gottfried yawned, and the number of people in the crowd, P_{\text{minute}}(t)Pminute(t)P, start subscript, start text, m, i, n, u, t, e, end text, end subscript, left parenthesis, t, right parenthesis, who yawned as a result is modeled by the following function: Pminute(t)=5⋅(1.03)
Every hour, the number of people who yawn in Gottfried's experiment grows by a factor of 5.89
After a certain medicine is ingested, its concentration in the bloodstream changes over time. C(t)=95⋅(0.87)t
Every minute, the concentration of the medicine shrinks by a factor of .87.
Qiaochu invested some money in a bank account. The relationship between the elapsed time, ttt, in months, since Qiaochu invested the money, and the total amount of money in the account, M(t)M(t)M, left parenthesis, t, right parenthesis, in dollars, is modeled by the following function: M(t)=3200⋅(1.02)t
Every month, 2 percent of money is added to the total amount of money in the account.
Pavlo invested some money in a bank account. The relationship between the elapsed time, ttt, in months, since Pavlo invested the money, and the total amount of money in the account, M(t)M(t)M, left parenthesis, t, right parenthesis, in dollars, is modeled by the following function: M(t)=1000⋅(1.01)t
Every month, the amount of money in the account grows by a factor of 1.01
After a certain medicine is ingested, the number of harmful bacteria remaining in the body declines rapidly. The relationship between the elapsed time ttt, in minutes, since the medicine is ingested, and the number of harmful bacteria remaining in the body, H_{\text{minute}}(t)Hminute(t)H, start subscript, start text, m, i, n, u, t, e, end text, end subscript, left parenthesis, t, right parenthesis, is modeled by the following function: H_{\text{minute}}(t)=500{,}000{,}000\cdot (0.2)^{t}Hminute(t)=500,000,000⋅(0.2)t
Every second, the number of harmful bacteria remaining in the body decays by a factor of .97
After a special medicine is introduced into a petri dish full of bacteria, the number of bacteria remaining in the dish decreases rapidly. The relationship between the elapsed time ttt, in seconds, and the number of bacteria, B(t)B(t)B, left parenthesis, t, right parenthesis, in the petri dish is modeled by the following function: B(t)=6400⋅(0.81)t4
Every second, there is a 5%percent removal from the total number of bacteria in the Petri dish.
Ocean sunfishes are well-known for rapidly gaining a lot of weight on a diet based on jellyfish. The relationship between the elapsed time, ttt, in days, since an ocean sunfish is born, and its mass, M_{\text{day}}(t)Mday(t)M, start subscript, start text, d, a, y, end text, end subscript, left parenthesis, t, right parenthesis, in milligrams, is modeled by the following function: Mday(t)=3.5⋅(1.05)t
Every week, the mass of the sunfish increases by a factor of 1.41
On the first day of spring, an entire field of flowering trees blossoms. The population of locusts consuming these flowers rapidly increases as the trees blossom. The relationship between the elapsed time, ttt, in days, since the beginning of spring, and the total number of locusts, N_{\text{day}}(t)Nday(t)N, start subscript, start text, d, a, y, end text, end subscript, left parenthesis, t, right parenthesis, is modeled by the following function: Nday(t)=300⋅(1.2)t
Every week, the number of locusts grows by a factor of 3.583.583, point, 3.58.
Bharat sent a chain letter to his friends, asking them to forward the letter to more friends. The relationship between the elapsed time ttt, in days, since Bharat sent the letter, and the number of people, P(t)P(t)P, left parenthesis, t, right parenthesis, who receive the email is modeled by the following function: P(t)=2401⋅(87)t1.75
The group of people who receive the email gains \dfrac{1}{7}71start fraction, 1, divided by, 7, end fraction of its size every 1.75 days.
A sample of an unknown chemical element naturally loses its mass over time. The relationship between the elapsed time ttt, in months, since the mass of the sample was initially measured, and its mass, M(t)M(t)M, left parenthesis, t, right parenthesis, in grams, is modeled by the following function: M(t)=120⋅(81625)t
The mass of the sample decreases by a factor of \dfrac 3553start fraction, 3, divided by, 5, end fraction every 0.250.250, point, .25 months
The relationship between the elapsed time, ttt, in seconds, since the food was introduced, and the total number of bacteria, N(t)N(t)N, left parenthesis, t, right parenthesis, is modeled by the following function: N(t)=1000⋅8t
The number of bacteria is doubled every .33 seconds
On the first day of spring, an entire field of flowering trees blossoms. The population of locusts consuming these flowers rapidly increases as the trees blossom. The relationship between the elapsed time, ttt, in weeks, since the beginning of spring, and the total number of locusts, N(t)N(t)N, left parenthesis, t, right parenthesis, is modeled by the following function: N(t)=300⋅(4916)t
The population of locusts gains 3/4 of its size every .5 weeks.
A sample of an unknown chemical element naturally loses its mass over time. The relationship between the elapsed time ttt, in days, since the mass of the sample was initially measured, and its mass, M(t)M(t)M, left parenthesis, t, right parenthesis, in grams, is modeled by the following function: M(t)=900⋅(827)t
The sample loses \dfrac{1}{3}31start fraction, 1, divided by, 3, end fraction of its mass every .33 days.
The chemical element einsteinium-253253253 naturally loses its mass over time. A sample of einsteinium-253253253 had an initial mass of 320320320 grams when we measured it. The relationship between the elapsed time ttt, in days, and the mass, M(t)M(t)M, left parenthesis, t, right parenthesis, in grams, left in the sample is modeled by the following function: M(t)=320⋅(0.125)t61.4
The sample loses of its mass every days 61.4
After a special medicine is introduced into a petri dish full of bacteria, the number of bacteria remaining in the dish decreases rapidly. The relationship between the elapsed time ttt, in seconds, and the number of bacteria, B_{\text{second}}(t)Bsecond(t)B, start subscript, start text, s, e, c, o, n, d, end text, end subscript, left parenthesis, t, right parenthesis, in the petri dish is modeled by the following function: Bsecond(t)=6000⋅(1516)t
every minute decays .02
Cleopatra uploaded a funny cat video on her website, which rapidly gains views over time. The relationship between the elapsed time, ttt, in days, since Cleopatra uploaded the video, and the total number of views, V(t)V(t)V, left parenthesis, t, right parenthesis, is modeled by the following function: Vday(t)=580⋅(1.17)t
every week, the number of views grows by a factor of 3
The number of exercises on Khan academy has increased rapidly since it began in 200620062006. The relationship between the elapsed time, ttt, in years, since Khan academy began, and the total number of its exercises, E_{\text{year}}(t)Eyear(t)E, start subscript, start text, y, e, a, r, end text, end subscript, left parenthesis, t, right parenthesis, is modeled by the following function: Eyear(t)=100⋅(1.7)t
month 1.05
Satoshi 24 2 t/15
triples every 15 years