The population of Springville is currently 2000 and doubles every 15 years. This

Question

The population of Springville is currently 2000 and doubles every 15 years. This means that after 15 years there are 1000 people, after 30 years there are 8000 people, etc. a) Write an exponential function P(t) that gives the population of Springville after t years. b) How long will it take for the population to reach 5000? Give the exact answer in terms of logarithms. The population of Fallville is currently 1200 and triples every 10 years. a) Write an exponential function P(t) that gives the population of Fallville after t years. b) How long will it take for the population to reach 4500? Give the exact answer in terms of logarithms.

Explanation / Answer

1)

a)P(t)=2000 *2(t/15)

b) population =5000

2000 *2(t/15)=5000

2(t/15)=(5/2)

2(t/15)=2.5

t/15=log(2)2.5

t=15*log(2)(2.5) years

-----------------------------------

2)

a)P(t)=1200 *3(t/10)

b) population =4500

1200 *3(t/10)=4500

3(t/10)=45/12

3(t/10)=3.75

t/10=log(3)3.75

t=10*log(3)3.75 years

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.