Question

The exponential decay graph shows the expected depreciation for a new boat, selling for $3500, over 10 years.

a. Write an exponential function for the graph.
b. Use the function in part a to find the value of the boat after 9.5 years.


Answer 1

There's an equation for exponential growth and decay, you remember what it was?

Answer 2

i think its y=c*e^rt ?

Answer 3

Or you can also use the equation y=ab^x
x = time, a = initial amount, and b = rate of exponential growth.

y = ab^x
a = 3500
when x=3, y = 1500
1500 = 3500b^3

Answer 4

the equation y=ab^x is easier to comprehend in my opinion

Answer 5

and from there solve for b

Answer 6

oh okay. because when i was working it out i was getting lost on my problem. so thank you.

Answer 7

what would the answer for be for b?

Answer 8

after solving the equation for 1500 = 3500b^3
you'll get the answer for b
from there
y = 3500(the answer for b)^9.5
x = time which is 9.5 for the second part

Answer 9

so would it be, y=3500(3/7)^9.5 or y(9.5)=3/7?

Answer 10

\[b =\sqrt[3]{\frac{ 3 }{ 7 }}\]

Answer 11

which is 0.753947441 in decimal form

Answer 12

y=ab^x
for part b
y = 3500(0.753947441)^9.5

Answer 13

that equals to?

Answer 14

so that would be the exact answer? with the decimal being that long?

Answer 15

whoops didn't see the last part. okay hold on

Answer 16

you're basically solving the outcome of that equation for part b

Answer 17

so 238.226?

Answer 18

i meant, 239.226

Answer 19

for part A, in the graph where i looked at year 3, the amount is 1500
so by using the equation y=ab^x
x is time, and for x i got 3
when x=3 y is therfore 1500
1500 = 3500b^3
the initial amount in (a) stays the same
and yes you are correct, its 239.226

Answer 20

yay! so b is 239.226?

Answer 21

if so thank you so much for your help!

Answer 22

You're Welcome :)