# Math Help - Economics consumption spending.

1. ## Economics consumption spending.

The function $C = 500(1-e^{-0.3x})$ shows individual consumption spending (C) in $as a function of income (x) in$000. At what income level will and individual have consumption spending of $400? You may find it helpful to use the fact that ln0.2 =-1.609 to 3dp. Could someone please walk me through how i work these questions out , they really stump me. Thanks. 2. Originally Posted by el123 I had this question in a test and had no idea how to answer it. The function $C = 500(1-e^{-0.3x})$ shows individual consumption spending (C) in$ as a function of income (x) in $000. At what income level will and individual have consumption spending of$400? You may find it helpful to use the fact that ln0.2 =-1.609 to 3dp.

Could someone please walk me through how i work these questions out , they really stump me.

Thanks.
Solve $400 = 500(1-e^{-0.3x})$ for x. Then multiply x by 1000.

3. ok so so far i have got

$400 = 500(1-e^{-0.3x})$

$400=500-500e^{-0.3x}$

$400 + 500e^{-0.3x} = 500$

$500e^{-0.3x} = 500-400$

$\frac{500e^{-0.3x}}{500}=\frac{100}{500}$

$e^{-0.3x} = \frac{1}{5}$

Thats where i get stuck , i don't know how to deal with the e. Get's me every time.

4. ok so i tried this is this correct?

$x=\frac{\ln{\frac{1}{5}} }{-0.3}$

5. Originally Posted by el123
ok so i tried this is this correct?

$x=\frac{\ln{\frac{1}{5}} }{-0.3}$
Correct. And you're told that ln0.2 =-1.609 ....