Write the equation in exponentiai form. Assume that ail constants are positive and not equal to 1. logy(8) = q \fFind the Largest value of it: that satisfies: log5[m)log5(:13+4)=5 1132' n .I III lInnl A bank features a savings account that has an annual percentage rate of T = 4.8% with interest compounded quarterly. Leslie deposits $5,005] into the account. 31 n! The account balance can be modeled by the exponential formula 3(15) = P(1 + ) , where S is the 11 future value, Pis the present value, a" is the annual percentage rate written as a decimal, n is the number of times each year that the interest is compounded, and t is the time in years. [A] What values should be used for P, r, and n? P=| L r=| L n=| | {B} How much money will Leslie have in the account in 1'1] years? Answer = 5| |. Round answer to the nearest penny. If 30600 dollars is invested at an interest rate of 9 percent per year, find the value of the investment at the end of 5 years for the following compounding methods. (a) Annual: Your answer isI I (b) Semiannual: Your answer is I I {c} Monthly: Your answer is I I {d} Daily: Your answer is I I You deposit $2000 in an account earning 8% interest compounded monthly. How much will you have in the account in 15 years? 51 Complete the table below giving the amount P that must be invested at interest rate 8 96 compounded continuously to obtain a balance of A = 5 190000 in t years. Round your answer to the nearest cent or two decimal places. t | P | 50 | | Find the time it takes for $5,700 to double when invested at an annual interest rate of 39:3, compounded continuously. ' lyears Find the time it takes for $570,000 to double when invested at an annual interest rate of 396, compounded continuously. ' ' years Give your answers accurate to 4 decimal places. The number of bacteria in a culture is given by the function Mt) = 97030.3: where t is measured in hours. {a} What is the relative rate of growth of this bacterium population? Your answer is | | percent {b} What is the initial population of the culture {at t=]? Your answer is | | {c} How mam,-r bacteria will the culture contain at time t=53 Your answer is | | \fA population of bacteria is growing according to the equation PH} : 1750302\". Estimate when the population will exceed 3356. Give 1your answer accurate to at least one decimal place. A bacteria culture starts with 720 bacteria and grows at a rate proportional to its size. After 5 hours there will be 3600 bacteria. [a] Express the population P after t hours as a function of t. Be sure to keep at least 4 significant figures on the growth rate. Plti=| l (b) What will be the population after 6 hours? _- I l bacteria {:2} How long will it take for the population to reach 1RD? Give your answer accurate to at least 2 decimal places. I l hours An unknown radioactive element decay5 into nonradioactive 5ub5tance5. In 120 days the radioactivity of a sample decreases by 59 percent. (a) What is the halflife of the element? half- life: i i {days} (In) How long will it take for a sample of 100 mg to decay to 56 mg? time needed:' ' (days) The value of China's exports of automobiles and parts (in billions of dollars]I is approximately a\If legn: + 4) = 3, then m :- You mayr enter the exact 1value or round to 4 decimal pLaces. \fSolve for 3:: leg[:1': + 3) leg{:a | 2) = 2 $=| | You may enter the exact value or round to 4 decimal plaeea.