Write an exponential equation for the following scenario, $1000 is deposited into an account that earns 5% interest. a) y=1000(5) b) y=1000(.05)^2 c) y=1000(1.05)^x d) y=5(1000)^x

Adding 5% interest to an account yearly has the same effect as taking 105% of its current value every year (you're taking all of your money - 100% of it - and adding an extra 5%, getting you 100% + 5% = 105%). This means that, if we started with $1000, after the first year, we'd have

1000(1.05) = $1050

after the second, and third years

1000(1.05)(1.05) = 1000(1.05)² = $1102.50

1000(1.05)(1.05)(1.05) = 1000(1.05)³ ≈ $1157.62

We can see a pattern starting to emerge. The 1000 always stays the same since its our starting value, but the power of the 1.05 goes up by 1 every year. In general, if we call the current value of the account in dollars y and the number of years it's been in the account x, then we can write this pattern generally as

b

step-by-step explanation:

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47