Question

WILL MEDAL!!!!!!
1. Suppose that the population of deer in the state is 19,900 and is growing 3% each year. Predict the population after 10 years.
a. about 274,338 deer
b. about 26,744 deer
c. about 597,000 deer
d. about 204,970 deer

Find the balance in the account.
2. $3,300 principal earning 4%, compounded annually, after 3 years
a. $3,712.05
b. $211,200.00
c. $3,696.00
d. $10,296.00

3. $1,600 principal earning 7%, compounded semi-annually, after 33 years
a. $4,979.11
b. $14,920.54
c. $112,992.00
d. $15,494.70

Answer 1

If the population is growing 3% each year, then the population of deer at the end of each year will be 103% of the population at the start of the year. So, we can predict the population of deer for any year by setting up a formula. The formula should follow this pattern: p = p(i) * r^n where p(n) is the population after n years, p(i) is the initial population, r is the rate of growth, and n is the number of years after the initial population was recorded. So, the formula for calculating the population for n number of years is: p(n) = 19,900 * 1.03^n Because we want to predict the population after 10 years, we should substitute 10 for n in the formula. p(10) = 19,900 * 1.03^10 Now, we simplify. p(10) = 19,900 * 1.3439 p(10) = 26743.935 Because you can't have a fraction of deer, we must round the answer down. So, the deer population after 10 years is 26,743. Hope this helps.